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Addendum Bibliography

Published online by Cambridge University Press:  19 December 2020

Douglas Lind  and
Brian Marcus
Douglas Lind
Affiliation:
University of Washington
Brian Marcus
Affiliation:
University of British Columbia, Vancouver
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An Introduction to Symbolic Dynamics and Coding , pp. 531 - 540
Publisher: Cambridge University Press
Print publication year: 2021

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References

[AbrK] Abrams, Adam and Katok, Svetlana, Adler and Flatto revisited: cross-sections for geodesic flow on compact surfaces of constant negative curvature, Studia Math. 246 (2019), 167–202.CrossRefGoogle Scholar
[AdaBMP] Adams, Stefan, Briceño, Raimundo, Marcus, Brian, and Pavlov, Ronnie, Representation and poly-time approximation for pressure of Z2 lattice models in the non-uniqueness region, J. Stat. Phys. 162 (2016), 1031–1067.Google Scholar
[Adl] Adler, Roy L., Symbolic dynamics and Markov partitions, Bull. Amer. Math. Soc. (N.S.) 35 (1998), 1–56.Google Scholar
[AirBL] Airey, Dylan, Bowen, Lewis, and Lin, Frank, A topological dynamical system with two different positive sofic entropies, arXiv:1911.08272.Google Scholar
[AllAY] Allahbakhshi, Mahsa, Antonioli, John, and Yoo, Jisang, Relative equilibrium states and class degree, Ergodic Theor. Dyn. Syst. 39 (2019), 865–888.CrossRefGoogle Scholar
[AllHJ] Allahbakhshi, Mahsa, Hong, Soonjo, and Jung, Uijin, Structure of transition classes for factor codes on shifts of finite type, Ergodic Theor. Dyn. Syst. 35 (2015), 2353–2370.Google Scholar
[AllQ] Allahbakhshi, Mahsa and Quas, Anthony, Class degree and relative maximal entropy, Trans. Amer. Math. Soc 365 (2013), 1347–1368.Google Scholar
[AlmCKP] Almeida, Jorge, Costa, Alfredo, Kyriakoglou, Revekka, and Perrin, Dominique, Profinite Semigroups and Symbolic Dynamics, Springer Lecture Notes in Mathematics (to appear).Google Scholar
[AshJMS] Ashley, J., Jaquette, G., Marcus, B., and Seeger, P., Runlength limited encoding/decoding with robust resync, United States Patent 5,696,649, 1999.Google Scholar
[AubBT] Aubrun, Nathalie, Barbieri, Sebastián, and Thomassé, Stéphan, Realization of aperiodic subshifts and uniform densities in groups, Groups Geom. Dyn. 13 (2019), 107–129.Google Scholar
[AubS] Aubrun, Nathalie and Sablik, Mathieu, Simulation of effective subshifts by two-dimensional subshifts of finite type, Acta Appl. Math. 126 (2013), 35–63.Google Scholar
[BakG] Baker, S. and Ghenciu, A.E., Dynamical properties of S-gap shifts and other shift spaces, J. Math. Anal. Appl. 430 (2015), 633–647.CrossRefGoogle Scholar
[BalS] Ballier, Alexis and Stein, Maya, The domino problem on groups of polynomial growth, Groups Geom. Dyn. 12 (2018), 93–105.CrossRefGoogle Scholar
[Barb] Barbieri, Sebastián, On the entropies of subshifts of finite type on countable amenable groups, arXiv:1905.10015.Google Scholar
[BarGMT] Barbieri, S., Gómez, R., Marcus, B., and Taati, S., Equivalence of relative Gibbs and relative equilibrium measures for actions of countable amenable groups, Nonlinearity 33 (2020), 2409–2454.Google Scholar
[Bart] Bartholdi, Laurent, Amenability of groups is characterized by Myhill’s theorem, J. Eur. Math. Soc. 21 (2019), 3191–3197.Google Scholar
[BarO] Barge, Marcy and Olimb, Carl, Asymptotic structure in substitution tiling spaces, Ergodic Theor. Dyn. Syst. 34 (2014), 55–94.CrossRefGoogle Scholar
[BarRYY] Barbero, A., Rosnes, E., Yang, G., and Ytrehus, O., Near-field passive RFID communication: channel model and code design, IEEE Trans. Commun. 62 (2014), 1716–1726.Google Scholar
[Bax1] Baxter, R. J., Exactly Solved Models in Statistical Physics, Academic Press, London, 1982.Google Scholar
[Bax2] Baxter, R. J., Planar lattice gases with nearest-neighbor exclusion, Ann. Comb. 3 (1999), 191–203.Google Scholar
[BefD] Beffara, Vincent and Duminil-Copin, Hugo, The self-dual point of the two-dimensional random-cluster model is critical for q ⩾ 1, Probab. Theory Relat. Fields 153 (2012), 511–542.Google Scholar
[Ber] Bernshteyn, Anton, Building large free subshifts using the Local Lemma, Groups Geom. Dyn. 13 (2019), 1417–1436.Google Scholar
[Bow1] Bowen, Lewis, A measure-conjugacy invariant for free group actions, Ann. of Math. (2) 171 (2010), 1387–1400.Google Scholar
[Bow2] Bowen, Lewis, Measure conjugacy invariants for actions of countable sofic groups, J. Amer. Math. Soc. 23 (2010), 217–245.Google Scholar
[Bow3] Bowen, Lewis, A brief introduction to sofic entropy theory, Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. III. Invited lectures, World Scientific Publications, Hackensack, NJ, 2018, pp. 1847–1866.Google Scholar
[BowR] Bowen, Rufus, Some systems with unique equilibrium states, Math. Systems Theory 8 (1974/75), 193–202.Google Scholar
[Boyd] Boyd, David, Irreducible polynomials with many roots of maximum modulus, Acta Arith. 68 (1994), 85–88.CrossRefGoogle Scholar
[Boy1] Boyle, Mike, Flow equivalence of shifts of finite type via positive factorizations, Pacific J. Math. 204 (2002), 273–317.CrossRefGoogle Scholar
[Boy2] Boyle, Mike, Some sofic shifts cannot commute with nonwandering shifts of finite type, Illinois J. Math. 48 (2004), 1267–1277.CrossRefGoogle Scholar
[Boy3] Boyle, Mike, Open problems in symbolic dynamics, Geometric and Probabilistic Structures in Dynamics, Contem. Math. 469, American Mathematical Society, 2008, pp. 69–118. Updates at www.math.umd.edu/∼mboyle/open.Google Scholar
[Boy4] Boyle, Mike, The work of Kim and Roush in symbolic dynamics, Acta Appl. Math. 126 (2013), 17–27.Google Scholar
[BoyBG] Boyle, Mike, Buzzi, Jerome, and Gómez, Ricardo, Almost isomorphism for countable state Markov shifts, J. Reine Angew. Math. 592 (2006), 23–47.Google Scholar
[BoyC] Boyle, Mike and Chuysurichay, Sompong, The mapping class group of a shift of finite type, J. Mod. Dynam. 13 (2018), 115–145.Google Scholar
[BoyCE1] Boyle, Mike, Carlsen, Toke Meier, and Eilers, Søren, Flow equivalence of sofic shifts, Israel J. Math. 225 (2018), 111–146.Google Scholar
[BoyCE2] Boyle, Mike, Carlsen, Toke Meier, and Eilers, Søren, Flow equivalence of G-shifts, arXiv:1512.05238v2 (2019).Google Scholar
[BoyD] Boyle, Mike and Downarowicz, Tomasz, The entropy theory of symbolic extensions, Invent. Math. 156 (2004), 119–161.Google Scholar
[BoyH] Boyle, Mike and Huang, Danrun, Poset block equivalence of integral matrices, Trans. Amer. Math. Soc. 355 (2003), 3861–3886.Google Scholar
[BoyL1] Boyle, Mike and Lind, Douglas, Expansive subdynamics, Trans. Amer. Math. Soc. 349 (1997), 55–102.Google Scholar
[BoyL2] Boyle, Mike and Lind, Douglas, Small polynomial matrix presentations of non-negative matrices, Linear Algebra Appl. 355 (2002), 49–70.Google Scholar
[BoyP] Boyle, Mike and Petersen, Karl, Hidden Markov processes in the context of symbolic dynamics, Entropy of Hidden Markov Processes and Connections to Dynamical Systems, LMS Lecture Note Ser. 385, Cambridge University Press, Cambridge, 2011, pp. 5–71.Google Scholar
[BoyPS] Boyle, Mike, Pavlov, Ronnie, and Schraudner, Michael, Multidimensional sofic shifts without separation and their factors, Trans. Amer. Math. Soc. 362 (2010), 4617–4653.Google Scholar
[BoyS1] Boyle, Mike and Schmieding, Scott, Symbolic dynamics and the stable algebra of matrices, arXiv:2006.01051.Google Scholar
[BoyS2] Boyle, Mike and Schraudner, Michael, Zd shifts of finite type without equal entropy full shift factors, J. Difference Equ. Appl. 15 (2009), 47–52.Google Scholar
[BoyS3] Boyle, Mike and Sullivan, Michael C., Equivariant flow equivalence for shifts of finite type, by matrix equivalence over group rings, Prof. London. Math. Soc. (3) 91 (2005), 184–214.Google Scholar
[Bre] Bremont, Julien, Gibbs measures at temperature zero, Nonlinearity 16 (2003), 419–426.Google Scholar
[Bri1] Briceño, Raimundo, The topological strong spatial mixing property and new conditions for pressure approximation, Ergodic Theor. Dyn. Syst. 38 (2018), 1658– 1696.Google Scholar
[Bri2] Briceño, Raimundo, An SMB approach for pressure representation in amenable virtually orderable groups, J. Anal. Math., to appear.Google Scholar
[BriMP] Briceño, Raimundo, McGoff, Kevin, and Pavlov, Ronnie, Factoring onto Zd subshifts with the finite extension property, Proc. Amer. Math. Soc. 146 (2018), 5129–5240.Google Scholar
[Bru] Brunotte, Horst, Algebraic properties of weak Perron numbers, Tatra Mt. Math. Publ. 56 (2013), 27–33.Google Scholar
[BurP] Burton, Robert and Pemantle, Robin, Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances, Ann. Prob. 21 (1993), 1329–1371.Google Scholar
[BurS] Burton, R. and Steif, J., Nonuniqueness of measures of maximal entropy for subshifts of finite type, Ergodic Theor. Dyn. Syst. 14 (1994), 213–235.Google Scholar
[Buz] Buzzi, Jérôme, Maximal entropy measures for piecewise affine surface diffeomorphisms, Ergodic Theor. Dyn. Syst. 29 (2009), 1723–1763.Google Scholar
[CalH] Calegari, Frank and Huang, Zili, Counting Perron numbers by absolute value, J. London Math. Soc. (2) 96 (2017), 181–200.Google Scholar
[Cap] Capocaccia, D., A definition of Gibbs state for a compact set with Zν action, Commun. Math. Phys. 48 (1976), 85–88.Google Scholar
[CapL] Capraro, Valerio and Lupini, Martino, Introduction to Sofic and Hyperlinear Groups and Connes’ Embedding Conjecture, Lecture Notes in Math. 2136, Springer, Heidelberg, 2015.Google Scholar
[CecC1] Ceccherini-Silberstein, Tullio and Coornaert, Michel, Cellular Automata and Groups, Springer, New York, 2012.Google Scholar
[CecC2] Ceccherini-Silberstein, Tullio and Coornaert, Michel, On the density of periodic configurations in strongly irreducible subshifts, Nonlinearity 25 (2012), 2119– 2131.Google Scholar
[CecMS] Ceccherini-Silberstein, T. G., Machì, A., and Scarabotti, F., Amenable groups and cellular automata, Ann. Inst. Fourier (Grenoble) 49 (1999), 673–685.Google Scholar
[Cha] Chandgotia, Nishant, Generalisation of the Hammersley–Clifford theorem on bipartite graphs, Trans. Amer. Math. Soc. 369 (2017), 7107–7137.Google Scholar
[ChaM] Chandgotia, Nishant and Meyerovitch, Tom, Markov random fields, Markov cocycles and the 3-colored chessboard, Israel J. Math. 215 (2016), 909–964.Google Scholar
[ChaCS] Chayes, J. T., Chayes, L., and Schonmann, R. H., Exponential decay of connectivities in the two-dimensional Ising model, J. Stat. Phys. 49 (1987), 433–445.Google Scholar
[ChaGU] Chazottes, J.-R., Gambaudo, J.-M., and Ugalde, E., Zero-temperature limit of one-dimensional Gibbs states via renormalization: the case of locally constant potentials, Ergodic Theor. Dyn. Syst. 31 (2011), 1109–1161.Google Scholar
[ChaH] Chazottes, J.-R. and Hochman, M., On the zero-temperature limit of Gibbs states, Commun. Math. Phys, 297 (2010), 265–281.Google Scholar
[ChaK] Chazottes, J.-R. and Keller, G., Pressure and Equilibrium States in Ergodic Theory, Mathematics of Complexity and Dynamical Systems. Vols. 1–3, Springer, New York, 2012, 1422–1437.Google Scholar
[ChaR1] Chan, Yao-Ban and Rechnitzer, Andrew, Accurate lower bounds on 2-D constraint capacities from corner transfer matrices, IEEE Trans. Inform. Theory 60 (2014), 3845–3858.CrossRefGoogle Scholar
[ChaR2] Chan, Yao-Ban and Rechnitzer, Andrew, Upper bounds on the growth rates of independent sets in two dimensions via corner transfer matrices, Linear Algebra Appl. 555 (2018), 139–156.Google Scholar
[ChaU1] Chazottes, J.-R. and Ugalde, E., Projection of Markov measures may be Gibbsian, J. Stat. Phys. 111 (2003), 1245–1272.Google Scholar
[ChaU2] Chazottes, J.-R. and Ugalde, E., On the preservation of Gibbsianness under symbol amalgamation, Entropy of Hidden Markov Processes and Connections to Dynamical Systems, LMS Lecture Note Ser. 385, Cambridge University Press, Cambridge, 2011, pp. 72–97.Google Scholar
[CheHLL] Chen, Hung-Hsun, Hu, Wen-Guei, Lai, De-Jan, and Lin, Song-Sun, Nonemptiness problems of Wang tiles with three colors, Theoretical Comput Sci. 547 (2014), 34–45.Google Scholar
[Cip] Cipra, Barry, An introduction to the Ising model, Amer. Math. Monthly 94 (1987), 937–959.Google Scholar
[ClmT1] Climenhaga, Vaughn and Thompson, Daniel J., Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors, Israel J. Math. 192 (2012), 785–817.CrossRefGoogle Scholar
[ClmT2] Climenhaga, Vaughn and Thompson, Daniel J., Equilibrium states beyond specification and the Bowen property, J. Lond. Math. Soc. (2) 87 (2013), 401–427.Google Scholar
[Coh] Cohen, David Bruce, The large scale geometry of strongly aperiodic subshifts of finite type, Adv. Math. 308 (2017), 599–626.Google Scholar
[CohEP] Cohen, C., Elkies, N., and Propp, J., Local statistics for random domino tilings of the Aztec diamond, Duke Math. J. 85 (1996), 117–166.Google Scholar
[CovN] Coven, Ethan M. and Nitecki, Zbigniew, On the genesis of symbolic dynamics as we know it, Colloq. Math. 110 (2008), 227–242.Google Scholar
[CyrFKP] Cyr, Van, Franks, John, Kra, Bryna, and Petite, Samuel, Distortion and the automorphism group of a shift, J. Mod. Dyn. 13 (2018), 147–161.Google Scholar
[CyrK1] Cyr, Van and Kra, Bryna, Nonexpansive Z2-subdynamics and Nivat’s Conjecture, Trans. Amer. Math. Soc. 367 (2015), 6487–6537.Google Scholar
[CyrK2] Cyr, Van and Kra, Bryna, The automorphism group of a shift of linear growth: beyond transitivity, Forum Math. Sigma 3 (2015), e5, 27pp.CrossRefGoogle Scholar
[CyrK3] Cyr, Van and Kra, Bryna, The automorphism group of a shift with subquadratic growth, Proc. Amer. Math. Soc. 144 (2016), 513–621.Google Scholar
[CyrK4] Cyr, Van and Kra, Bryna, Complexity of short rectangles and periodicity, J. Eur. Comb. 52 (2016), 146–173.Google Scholar
[CyrK5] Cyr, Van and Kra, Bryna, The automorphism group of a minimal shift of stretched exponential growth, J. Mod. Dyn. 10 (2016), 483–495.Google Scholar
[CyrK6] Cyr, Van and Kra, Bryna, The automorphism group of a shift of slow growth is amenable, Ergodic Theor. Dyn. Syst. (to appear).Google Scholar
[Dav] Davis, Diana, Cutting sequences on translation surfaces, New York J. Math. 20 (2014), 399–429.Google Scholar
[Den] Deninger, Christopher, Fuglede-Kadison determinants and entropy for actions of discrete amenable groups, J. Amer. Math. Soc. 19 (2006), 737–758.Google Scholar
[Des1] Desai, Angela, Subsystem entropy for Zd-sofic shifts, Indag. Mathem. 17 (2006), 353–359.Google Scholar
[Des2] Desai, Angela, A class of Zd shifts of finite type which factors onto lower entropy full shifts, Proc. Amer. Math. Soc. 137 (2009), 2613–2621.Google Scholar
[Dob] Dobrushin, R., Description of a random eld by means of conditional probabilities and conditions for its regularity, Teor. Verojatnost. i Primenen 13 (1968), 201– 229.Google Scholar
[DonDMP] Donoso, Sebastian, Durand, Fabien, Maass, Alejandro, and Samuel Petite, On automorphism groups of Toeplitz subshifts, Discrete Anal. (2017), Paper no. 11, 19 pp.Google Scholar
[Dow] Downarowicz, Tomasz, Entropy in Dynamical Systems, New Mathematical Monographs 18, Cambridge University Press, Cambridge, 2011.Google Scholar
[DurP] Durand, Fabien and Perrin, Dominique, Dimension Groups and Dynamical Systems, Cambridge University Press (to appear).Google Scholar
[DurRS] Durand, Bruno, Romaschenko, Andrei, and Shen, Alexander, Fixed-point tile sets and their applications, J. Comput. System Sci. 78 (2012), 731–764.Google Scholar
[Dye] Dye, H., On groups of measure preserving transformations I, Amer. J. Math. 81 (1959), 119–159; II 85 (1963), 551–576.Google Scholar
[EilK] Eilers, Søren and Kiming, Ian, On some new invariants for shift equivalence for shifts of finite type, J. Number Theory 132 (2012), 502–510.Google Scholar
[EilRRS] Eilers, Søren, Restorff, Gunnar, Ruiz, Efren, and Sørensen, Adam P. W., Geometric classification of graph C∗-algebras over finite graphs, Canad. J. Math. 70 (2018), 294–353.Google Scholar
[Ein] Einsiedler, Manfred, Fundamental cocycles and tiling spaces, Ergodic Theor. Dyn. Syst. 21 (2001), 777–800.Google Scholar
[EinL] Einsiedler, Manfred and Lind, Douglas, Algebraic Zd-actions of entropy rank one, Trans. Amer. Math. Soc. 356 (2004), 1799–1831.Google Scholar
[EinS] Einsiedler, M. and Schmidt, K., Markov partitions and homoclinic points of algebraic Zd-actions, Proc. Steklov Inst. Math. 1997 (216), 259–279.Google Scholar
[EliMS] Elishco, O., Meyerovitch, T., and Schwartz, M., Semiconstrained systems, IEEE Trans. Inform. Theory 62 (2016), 1688–1702.Google Scholar
[EntR] van Enter, A. C. D. and Ruszel, W. M., Chaotic temperature dependence at zero temperature, J. Stat. Phys. 2007 (127), 567–573.Google Scholar
[EpiKM] Epifanio, Chiara, Koskas, Michel, and Mignosi, Filippo, On a conjecture in bidimensional words, Theoret. Comput. Sci. 299 (2003), 123–150.Google Scholar
[ExeL] Exel, Ruy and Laca, Marcelo, The K-theory of Cuntz-Krieger algebras for infinite matrices, J. Reine Angew. Math. 512 (1999), 119–172.Google Scholar
[FreOP] French, Thomas, Ormes, Nic, and Pavlov, Ronnie, Subshifts with slowly growing numbers of follower sets, Contemp. Math. 678 (2016), 192–203.Google Scholar
[Frie] Fried, David, Ideal tilings and symbolic dynamics for negatively curved surfaces, Ergodic Theor. Dyn. Syst. 31 (2011), 1697–1726.Google Scholar
[Fri] Friedland, Shmuel, On the entropy of Zd subshifts of finite type, Linear Algebra Appl. 252 (1997), 199–220.Google Scholar
[FriLM] Friedland, Shmuel, Lundlow, Per Håkan, and Markström, Klas, The 1-vertex transfer matrix and accurate estimation of channel capacity, IEEE Trans. Inform. Theory 56 (2010), 3692–3699.Google Scholar
[FriP] Friedland, Shmuel and Peled, Uri, The pressure, densities and first-order phase transitions associated with multidimensional SOFT, Trends in Mathematics, BirkhuserSpringer, Basel, 2011, pp. 179–220.Google Scholar
[FriST] Frisch, Joshua, Schlank, Tomer, and Tamuz, Omer, Normal amenable subgroups of the automorphism group of the full shift, Ergodic Theor. Dyn. Syst. 39 (2019), 1290–1298.Google Scholar
[Fro] Frongillo, Rafael, Optimal state amalgamation is NP-hard, Ergodic Theor. Dyn. Syst. 39 (2019), 1857–1869.Google Scholar
[GamK] Gamarnik, David and Katz, Dmitriy, Sequential cavity method for computing free energy and surface pressure, J. Stat. Phys. 137 (2009), 205–232.Google Scholar
[GanH] Gangloff, Silvère and de Menibus, Benjamin Hellouin, Effect of quantified irre-ducibility on the computability of subshift entropy, Discrete Contin. Dyn. Syst. 39 (2019), 1975–2000.Google Scholar
[GaoJS1] Gao, Su, Jackson, Steve, and Seward, Brandon, A coloring property for countable groups, Math. Proc. Camb. Philos. Soc. 147 (2009), 579–592.Google Scholar
[GaoJS2] Gao, Su, Jackson, Steve, and Seward, Brandon, Group Colorings and Bernoulli Subflows, Mem. Amer. Math. Soc. 241, American Mathematical Society, 2016.Google Scholar
[GeoHM] Georgii, Hans-Otto, Häggström, Olle, and Maes, Christian, The random geometry of equilibrium phases, Phase Transit. Crit. Phenom. 18, Academic Press, San Diego, 2001, pp. 1–142.Google Scholar
[GioMPS] Giordano, Thierry, Matui, Hiroki, Putnam, Ian, and Skau, Christian, Orbit equivalence for Cantor minimal Zd-systems, Invent. Math. 179 (2010), 119–158.Google Scholar
[GioPS] Giordano, Thierry, Putnam, Ian, and Skau, Christian, Topological orbit equivalence and C∗-crossed products, J. Reine Angew. Math. 469 (1995), 51–111.Google Scholar
[Got] Gottschalk, Walter, Some general dynamical notions, Recent Advances in Topological Dynamics, Lecture Notes in Math. 138, Springer, Berlin, pp. 120–125.Google Scholar
[Gri] Grimmett, Geoffrey, Probability on Graphs, 2nd Edition, Cambridge University Press, Cambridge, 2018.Google Scholar
[GriM] Grigorchuk, Rostislav I. and Medynets, Konstantin, On algebraic properties of topological full groups, arXiv:1105.0719v4.Google Scholar
[Gro] Gromov, M., Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. 1 (1999), 109–197.Google Scholar
[HamC] Hammersley, J. M. and Clifford, P., Markov fields on finite graphs and lattices, 1968, www.statslab.cam.ac.uk/∼grg/books/hammfest/hamm-cliff.pdf.Google Scholar
[Hay] Hayes, Ben, Fuglede-Kadison determinants and sofic entropy, Geom. Funct. Anal. 26 (2016), 520–606.CrossRefGoogle Scholar
[Hoc1] Hochman, Michael, On the dynamics and recursive properties of multidimensional symbolic systems, Invent. Math. 176 (2009), 131–167.Google Scholar
[Hoc2] Hochman, Michael, On the automorphism groups of multidimensional shifts of finite type, Ergodic Theor. Dyn. Syst. 30 (2010), 809–840.Google Scholar
[Hoc3] Hochman, Michael, Non-expansive directions for Z2 actions, Ergodic Theor. Dyn. Syst. 31 (2011), 91–112.Google Scholar
[Hoc4] Hochman, Michael, Multidimensional shifts of finite type and sofic shifts, Combinatorics, Words and Symbolic Dynamics (Valérie Berthé and Michel Rigo, eds.), Cambridge University Press, Cambridge, 2016, pp. 296–358.Google Scholar
[HocM] Hochman, Michael and Meyerovitch, Tom, A characterization of the entropies of multidimensional shifts of finite type, Ann. Math. 171 (2010), 2011–2038.Google Scholar
[Hon] Hong, S., Loss of Gibbs property in one-dimensional mixing shifts of finite type, Qual. Theory of Dynam. Sys. 19 (2020), 21pp.Google Scholar
[HosP] Host, B. and Parreau, F., Homomorphismes entre systèmes dynamiques définis par substitutions, Ergodic Theor. Dyn. Syst. 9 (1989), 469–477.Google Scholar
[Imm1] Immink, K. A. S., EFMPlus, 8–16 modulation code, United States Patent Number 5,696,505.Google Scholar
[Imm2] Immink, K. A. S., Codes for Mass Data Storage Systems, 2nd Edition, Shannon Foundation Publishers, Eindhoven, The Netherlands, 2004.Google Scholar
[Jea1] Jeandel, Emmanuel, Computability in symbolic dynamics, Pursuit of the Universal (Lecture Notes in Computer Science), Springer, 2016, pp. 124–131.Google Scholar
[Jea2] Jeandel, Emmanuel, Aperiodic subshifts on nilpotent and polycyclic groups, arXiv: 1510.02360v2.Google Scholar
[Jea3] Jeandel, Emmanuel, Aperiodic subshifts of finite type on groups, arXiv:1501.06831.Google Scholar
[Jea4] Jeandel, Emmanuel, Strong shift equivalence as a categorical notion, Preprint (2020), 23 pp.Google Scholar
[JeaV1] Jeandel, Emmanuel and Vanier, Pascal, Hardness of conjugacy, embedding and factorization of multidimensional subshifts, J. Comput. System Sci. 81 (2015), 1648–1664.Google Scholar
[JeaV2] Jeandel, Emmanuel and Vanier, Pascal, Characterizations of periods of multidimensional shifts, Ergodic Theor. Dyn. Syst. 35 (2015), 431–460.Google Scholar
[JohM1] Johnson, Aimee and Madden, Kathleen, The decomposition theorem for two dimensional shifts of finite type, Proc. Amer. Math. Soc. 127 (1999), 1533–1543.Google Scholar
[JohM2] Johnson, Aimee and Madden, Kathleen, Factoring higher dimensional shifts of finite type onto the full shift, Ergodic Theor. Dyn. Syst. 25 (2005), 811–822.Google Scholar
[JusM] Juschenko, Kate and Monod, Nicolas, Cantor systems, piecewise translations and simple amenable groups, Ann. of Math. (2) 178 (2013), 775–787.Google Scholar
[Kar] Kari, Jarkko, Low-complexity tilings of the plane, Lecture Notes in Comput. Sci., Springer, Cham, 2019.CrossRefGoogle Scholar
[KarM] Kari, Jarkko and Moutot, Etienne, Nivat’s conjecture and pattern complexity in algebraic subshifts, Theoret. Comput. Sci. 777 (2019), 379–386.CrossRefGoogle Scholar
[KarS] Kari, Jarkko and Szabados, Michal, An algebraic geometric approach to Nivat’s conjecture, Inf. and Comp. 271 (2020), 104481.CrossRefGoogle Scholar
[Kat] Katok, Anatole, Fifty years of entropy in dynamics: 1958–2007, J. Mod. Dyn. 1 (2007), 545–596.Google Scholar
[KatU] Katok, Svetlana and Ugarcovici, Ilie, Symbolic dynamics for the modular surface and beyond, Bull. Amer. Math. Soc. (N.S.) 44 (2007), 87–132.Google Scholar
[Kel] Keller, Gerhard, Equilibrium States in Ergodic Theory, London Mathematical Society Student Texts, Cambridge University Press, 1998.Google Scholar
[Kem] Kempton, T., Factors of Gibbs measures for subshifts of finite type, Bull. London Math. Soc. 43 (2011), 751–764.Google Scholar
[Ken] Kenyon, Richard, The construction of self-similar tilings, Geom. Funct. Anal. 6 (1996), 471–488.Google Scholar
[KenS] Kenyon, Richard and Solomyak, Boris, On the characterization of expansion maps for self-affine tilings, Discrete Comput. Geom. 43 (2010), 577–593.Google Scholar
[KenV] Kenyon, Richard and Vershik, Anatoly, Arithmetic construction of sofic partitions of hyperbolic toral automorphisms, Ergodic Theor. Dyn. Syst. 18 (1998), 357–372.Google Scholar
[KerL] Kerr, David and Li, Hanfeng, Theory, Ergodic: Independence and Dichotomies, Springer, 2016.Google Scholar
[Kor] Korec, Ivan, Irrational speeds of configuration growth in generalized Pascal triangles, Theoret. Computer Sci. 112 (1993), 399–412.Google Scholar
[Kri] Krieger, Wolfgang, On images of sofic systems, arXiv:1101.1750v2.Google Scholar
[Li] Li, Hanfeng, Compact group automorphisms, addition formulas and Fuglede-Kadison determinants, Ann. of Math. (2) 176 (2012), 303–347.Google Scholar
[LiT] Li, Hanfeng and Thom, Andreas, Entropy, determinants, and L2-torsion, J. Amer. Math. Soc. 27 (2014), 239–292.Google Scholar
[Lie] Lieb, E. H., Exact solution of the problem of the entropy of two-dimensional ice, Phys. Rev. Lett. 18 (1967), 692–694.CrossRefGoogle Scholar
[Lig1] Lightwood, Sam, Morphisms form nonperiodic Z2 subshifts I, Ergodic Theor. Dyn. Syst. 23 (2003), 587–609.Google Scholar
[Lig2] Lightwood, Sam, Morphisms form nonperiodic Z2 subshifts II, Ergodic Theor. Dyn. Syst. 24 (2004), 1227–1260.Google Scholar
[LimS] Lima, Yuri and Sarig, Omri, Symbolic dynamics for three dimensional flows with positive topological entropy, J. Eur. Math. Soc. 21 (2019), 199–256.Google Scholar
[Lin] Lind, Douglas, Multi-dimensional symbolic dynamics, Symbolic Dynamics and its Applications, Proc. Sympos. Applied Mathematics, American Mathematical Society, 2004, pp. 61–79.Google Scholar
[LinS1] Lind, Douglas and Schmidt, Klaus, Homoclinic points of algebraic Zd-actions, J. Amer. Math. Soc. 12 (1999), 953–980.Google Scholar
[LinS2] Lind, Douglas and Schmidt, Klaus, A survey of algebraic actions of the discrete Heisenberg group, Russ. Math. Surv. 70 (2015), 657–714.Google Scholar
[LinS3] Lind, Douglas and Schmidt, Klaus, A Bernoulli algebraic action of a free group, arXiv:1905.09966v1.Google Scholar
[Mah] Mahler, K., An application of Jensen’s formula to polynomials, Mathematika 7 (1960), 98–100.Google Scholar
[MarP] Marcus, Brian and Pavlov, Ronnie, An integral representation for topological pressure in terms of conditional probabilities, Israel J. Math. 207 (2015), 395– 433.Google Scholar
[Mat1] Matsumoto, K., Presentations of subshifts and their topological conjugacy invariants, Documenta Math. 4 (1999), 285–340.Google Scholar
[Mat2] Bon, Nicolás Matte, Subshifts with slow complexity and simple groups with the Liouville property, Geom. Frunct. Anal. 24 (2014), 1637–1659.Google Scholar
[Mat3] Matui, Hiroki, Some remarks on topological full groups of Cantor minimal systems, Int. J. of Math. 17 (2006), 231–251.Google Scholar
[McgP] McGoff, Kevin and Pavlov, Ronnie, Factor maps and embeddings for random Zd shifts of finite type, Israel J. Math. 230 (2019), 239–273.Google Scholar
[MeeS] Meester, Ronald and Steif, Jeffrey, Higher dimensional subshifts of finite type, factor maps and measures of maximal entropy, Pacific J. Math. 200 (2001), 497–510.Google Scholar
[Mey] Meyerovitch, T., Gibbs and equilibrium measures for some families of subshifts, Ergodic Theor. Dyn. Syst. 33 (2013), 934–953.Google Scholar
[Mil] Milnor, John, On the entropy geometry of cellular automata, Complex Systems 2 (1988), 357–386.Google Scholar
[MosRW] Mossinghoff, Michael J., Rhin, Georges, and Wu, Qiang, Minimal Mahler measures, Experiment. Math. 17 (2008), 451–458.Google Scholar
[Nas] Nasu, M., Textile systems and one-sided resolving automorphisms and endomorphisms of the shift, Ergodic Theor. Dyn. Syst. 28 (2008), 167–209.Google Scholar
[NowW] Nowakowski, Richard and Winkler, Peter, Vertex-to-vertex pursuit in a graph, Discrete Math. 43 (1983), 235–239.Google Scholar
[Ons] Onsager, L., Crystal statistics. I. A two-dimensional model with an order-disorder transition, Phys. Rev. (2) 65 (1944), 117–149.Google Scholar
[OrmP] Ormes, Nic and Pavlov, Ronnie, Extender sets and multidimensional subshifts, Ergodic Theor. Dyn. Syst. 36 (2016), 908–923.Google Scholar
[OrnW] Ornstein, Donald and Weiss, Benjamin, Entropy and isomorphism theorems for actions of amenable groups, J. Anal. Math. 48 (1987), 1–141.Google Scholar
[Pav1] Pavlov, Ronnie, Approximating the hard square entropy constant with probabilistic methods, Ann. Prob. 40 (2012), 2362–2399.Google Scholar
[Pav2] Pavlov, Ronnie, On non-uniform specification and uniqueness of the equilibrium state in expansive systems, Nonlinearity 32 (2019), 2441–2460.Google Scholar
[PavS] Pavlov, Ronnie and Schraudner, Michael, Entropies realizable by block gluing shifts of finite type, J. Anal. Math. 126 (2015), 113–174.Google Scholar
[Pes] Pestov, Vladimir G., Hyperlinear and sofic groups: a brief guide, Bull. Symbolic Logic 14 (2008), 449–480.Google Scholar
[Pia] Piantadosi, Steven T., Symbolic dynamics on free groups, Discrete Contin. Dyn. Syst. 20 (2008), 725–738.Google Scholar
[Pir1] Piraino, M., Projections of Gibbs states for Hölder potenials, J. Stat. Phys. 170 (2018), 952–961.Google Scholar
[Pir2] Piraino, M., Single site factors of Gibbs measures, Nonlinearity 33 (2020), 742– 761.Google Scholar
[PolK] Pollicott, M. and Kempton, T., Factors of Gibbs measures for full shifts, Entropy of Hidden Markov Processes and Connections to Dynamical Systems, LMS Lecture Note Ser. 385, Cambridge University Press, Cambridge, 2011, pp. 246–257.Google Scholar
[Put] Putnam, Ian, Cantor Minimal Systems, University Lecture Series 70, American Mathematical Society, 2018.Google Scholar
[QuaT] Quas, Anthony and Trow, Paul, Subshifts of multidimensional shifts of finite type, Ergodic Theor. Dyn. Syst. 20 (2000), 859–874.Google Scholar
[QuaZ] Quas, Anthony and Zamboni, Luca, Periodicity and local complexity, Theoret. Comput. Sci. 319 (2004), 229–240.CrossRefGoogle Scholar
[RadS] Radin, Charles and Sadun, Lorenzo, Isomorphism of hierarchical structures, Ergodic Theor. Dyn. Syst. 21 (2001), 1239–1248.Google Scholar
[Rob] Arthur Robinson, E., Jr., Symbolic dynamics and tilings in Rd , Symbolic Dynamics and its Applications, Proceedings of Symposia in Applied Mathematics, American Mathematical Society, 2004, pp. 81–119.Google Scholar
[RotS] Roth, R. and Siegel, P., On parity-preserving constrained coding, Proc. Internat. Sympos. Information Theory (2018), IEEE, Piscataway, New Jersey, 1804–1808.Google Scholar
[Rue] Ruelle, D., Thermodynamic Formalism, 2nd Edition, (Update of 1st Edition from 1978), Cambridge University Press, Cambridge, 2004.Google Scholar
[Sab] Sablik, Mathieu, Directional dynamics for cellular automata: A sensitivity to initial condition approach, Theoret. Comput. Sci. 400 (2008), 1–18.Google Scholar
[Sal] Salo, Ville, Toeplitz subshift whose automorphism group is not finitely generated, Colloq. Math. 146 (2017), 53–76.Google Scholar
[SalT] Salo, Ville and Törmä, Ilkka, Block maps between primitive uniform and Pisot substitutions, Ergodic Theor. Dyn. Syst. 35 (2015), 2292–2310.Google Scholar
[SanT] Sander, J. W. and Tijdeman, R., The rectangle complexity of functions on two-dimensional lattices, Theoret. Comput. Sci. 270 (2002), 857–863.Google Scholar
[Sar1] Sarig, Omri, Symbolic dynamics for surface diffeomorphisms with positive entropy, J. Amer. Math. Soc. 26 (2013), 341–426.Google Scholar
[Sar2] Sarig, Omri, Thermodynamic formalism for countable Markov shifts, Proc. Sympos. Pure Math. 89, American Mathematical Society, Providence, R.I., (2015), 81–117.Google Scholar
[Schi] Schinzel, Andrzej, A class of algebraic numbers, Tatra Mt. Math. Publ. 11 (1997), 35–42.Google Scholar
[Sch1] Schmidt, Klaus, Tilings, fundamental cocycles and fundamental groups of symbolic Zd-actions, Ergodic Theor. Dyn. Syst. 18 (1998), 1473–1525.Google Scholar
[Sch2] Schmidt, Klaus, Quotients of l∞ (Z, Z) and symbolic covers of toral automorphisms, Representation Theory, Dynamical Systems, and Asymptotic Combinatorics, Amer. Math. Soc. Transl. Ser. 2, 217, 2006, pp. 223–246.Google Scholar
[Sch3] Schmidt, Klaus, Representations of toral automorphisms, Topology Appl. 205 (2016), 88–116.Google Scholar
[Schr] Schraudner, Michael, A matrix formalism for conjugacies of higher-dimensional shifts of finite type, Colloq. Math. 110 (2008), 493–515.Google Scholar
[SchY] Schmieding, Scott and Yang, Kitty, The mapping class group of a minimal shift, arXiv:1810.08847.Google Scholar
[Sep] Seppäläinen, Timo, Entropy, limit theorems, and variational principles for disordered lattice systems, Commun. Math. Phys. 171 (1995), 233–277.Google Scholar
[SidV] Siderov, N. and Vershik, A., Bijective arithmetic codings of hyperbolic automorphisms of the 2-torus, and binary quadratic forms, J. Dynam. Control Systems 4 (1998), 365–399.Google Scholar
[SilW1] Silver, Daniel S. and Williams, Susan G., Knot invariants from symbolic dynamical systems, Trans. Amer. Math. Soc. 351 (1999), 3243–3265.Google Scholar
[SilW2] Silver, Daniel S. and Williams, Susan G., An invariant of finite group actions on shifts of finite type, Ergodic Theor. Dyn. Syst. 25 (2005), 1985–1996.Google Scholar
[Sim] Simpson, Stephen G., Medvedev degrees of two-dimensional subshifts of finite type, Ergodic Theor. Dyn. Syst. 34 (2014), 679–688.Google Scholar
[SmiU] Smillie, John and Ulcigrai, Corinna, Beyond Sturmian sequences: coding linear trajectories in the regular octagon, Proc. Lond. Math. Soc. (3) 102 (2011), 291–340.Google Scholar
[Tho] Thomsen, Klaus, On the structure of a sofic shift space, Trans. Amer. Math. Soc. 356 (2004), 3557–3619.Google Scholar
[Thu1] Thurston, William, Groups, Tilings, and Finite State Automata, AMS Colloquium Lecture Notes, Boulder, CO, 1989.Google Scholar
[Thu2] Thurston, William P., Entropy in dimension one, Frontiers in Complex Dynamics, Princeton Math. Ser. 51, Princeton Univ. Press, Princeton, NJ, 2014, pp. 339–384.Google Scholar
[Verb] Verbitskiy, Evgeny, Thermodynamics of Hidden Markov Processes, Entropy of Hidden Markov Processes and Connections to Dynamical Systems, LMS Lecture Note Ser. 385, Cambridge Univ. Press, Cambridge, 2011, pp. 258–272.Google Scholar
[Vers] Vershik, A. M., Arithmetic isomorphism of hyperbolic automorphisms of a torus and of sofic shifts, Funktsional. Anal. i Prilozhen. 26 (1992), 22–27.Google Scholar
[Vol] Volkov, Mikhail, Synchronizing automata and the Černý Conjecture, Proc. 2nd Intl. Conf. Language and Automata Theory and Applications, Springer-Verlag Lecture Notes in Computer Science 5196, 2008, 11–27.Google Scholar
[Wag1] Wagoner, J. B., Strong shift equivalence theory and the shift equivalence problem, Bull. Amer. Math. Soc. (N.S.) 36 (1999), 271–296.Google Scholar
[Wag2] Wagoner, J. B., Strong shift equivalence theory, Symbolic Dynamics and its Applications, Proc. Sympos. Applied Mathematics, American Mathematical Society, 2004, pp. 121–154.Google Scholar
[Wan1] Wang, Hao, Proving theorems by pattern recognition II, Bell Syst. Tech. J. 40 (1961), 1–41.Google Scholar
[Wan2] Wang, Hao, Notes on a class of tiling problems, Fund. Math. 82 (1974), 295–305.Google Scholar
[Weis] Weiss, Benjamin, Sofic groups and dynamical systems, Sankhya Ser. A 62 (2000), 350–359.Google Scholar
[Weit] Weitz, Dror, Counting independent sets up to the tree threshold, Ann. Sympos. Theory of Computing (STOC) 38 (2006), 140–149.Google Scholar
[Yay] Yayama, Y., On factors of Gibbs measures for almost additive potentials, Ergodic Theor. Dyn. Syst. 36 (2016), 276–309.Google Scholar
[Yaz] Yazdi, Mehdi, Lower bound for the Perron-Frobenius degrees of Perron numbers, Ergodic Theor. Dyn. Syst. (to appear).Google Scholar
[Yoo] Yoo, Jisang, Decomposition of infinite-to-one factor codes and uniqueness of relative equilibrium states, J. Modern Dynamics 13 (2018), 271–284.Google Scholar
[Yuz] Yuzvinskii, S. A., Calculation of the entropy of a group-endomorphism (Russian), Sibirsk. Mat. Z. 8 (1967), 230–239, Engl. transl. Sib. Math. J. 8, 172–178 (1968).Google Scholar
[Zin] Zinoviadis, Charalampos, Hierarchy and expansiveness in two-dimensional subshifts of finite type, Ph. D. dissertation (2016), arXiv:1603.05464.Google Scholar
[Zor] Zorich, Anton, Flat surfaces, Frontiers in Number Theory, Physics, and Geometry I, Springer, Berlin, 2006, pp. 437–583.Google Scholar

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  • Addendum Bibliography
  • Douglas Lind, University of Washington, Brian Marcus, University of British Columbia, Vancouver
  • Book: An Introduction to Symbolic Dynamics and Coding
  • Online publication: 19 December 2020
  • Chapter DOI: https://doi.org/10.1017/9781108899727.017
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  • Addendum Bibliography
  • Douglas Lind, University of Washington, Brian Marcus, University of British Columbia, Vancouver
  • Book: An Introduction to Symbolic Dynamics and Coding
  • Online publication: 19 December 2020
  • Chapter DOI: https://doi.org/10.1017/9781108899727.017
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  • Addendum Bibliography
  • Douglas Lind, University of Washington, Brian Marcus, University of British Columbia, Vancouver
  • Book: An Introduction to Symbolic Dynamics and Coding
  • Online publication: 19 December 2020
  • Chapter DOI: https://doi.org/10.1017/9781108899727.017
Available formats
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