Meromorphic Dynamics Elliptic Functions with an Introduction to the Dynamics of Meromorphic Functions
Book contents
- Frontmatter
- Dedication
- Contents
- Contents of Volume I
- Preface
- Acknowledgments
- Introduction
- Part III Topological Dynamics of Meromorphic Functions
- Part IV Elliptic Functions: Classics, Geometry, and Dynamics
- Part V Compactly Nonrecurrent Elliptic Functions: First Outlook
- Part VI Compactly Nonrecurrent Elliptic Functions: Fractal Geometry, Stochastic Properties, and Rigidity
- Appendix A A Quick Review of Some Selected Facts from Complex Analysis of a One-Complex Variable
- Appendix B Proof of the Sullivan Nonwandering Theorem for Speiser Class S
- References
- Index of Symbols
- Subject Index
- References
References
Published online by Cambridge University Press: 20 April 2023
Book contents
- Frontmatter
- Dedication
- Contents
- Contents of Volume I
- Preface
- Acknowledgments
- Introduction
- Part III Topological Dynamics of Meromorphic Functions
- Part IV Elliptic Functions: Classics, Geometry, and Dynamics
- Part V Compactly Nonrecurrent Elliptic Functions: First Outlook
- Part VI Compactly Nonrecurrent Elliptic Functions: Fractal Geometry, Stochastic Properties, and Rigidity
- Appendix A A Quick Review of Some Selected Facts from Complex Analysis of a One-Complex Variable
- Appendix B Proof of the Sullivan Nonwandering Theorem for Speiser Class S
- References
- Index of Symbols
- Subject Index
- References
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- Meromorphic DynamicsElliptic Functions with an Introduction to the Dynamics of Meromorphic Functions, pp. 503 - 509Publisher: Cambridge University PressPrint publication year: 2023
References
Ahlfors, L., Bers, L., Riemann’s mapping theorem for variable metrics, Ann. Math. 72 (1960), 385–404. 23.2Google Scholar
Aaronson, J., Denker, M., Urbański, M., Ergodic theory for Markov fibered systems and parabolic rational maps, Trans. Am. Math. Soc. 337 (1993), 495–548. 12, 15.3, 22.1, 22.3Google Scholar
Ahlfors, L., Grunsky, H., Über die Blochsche Konstante, Math. Z. 42 (1937), 671–673. 23.2CrossRefGoogle Scholar
Ahlfors, L.V., Zur Theorie der Überlagerungsfl¨achen, Acta Math. 65 (1935), 157–194. 8.2, 13.1Google Scholar
Alexander, D.S., A History of Complex Dynamics from Schröder to Fatou and Julia, Springer Fachmedien Wiesbaden (1994). Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft (1994). Softcover reprint of the hardcover first edition (1994). 12, 8, 15.1.1CrossRefGoogle Scholar
Alexander, D.S., Iavernaro, F., Rosa, A., Early Days in Complex Dynamics: A History of Complex Dynamics in One Variable During 1906–1942, History of Mathematics, vol. 38, American Mathematical Society, London Mathematical Society (2012). 12, 8Google Scholar
Armitage, J.V., Eberlein, W.F., Elliptic Functions, London Mathematical Society Student Texts, Cambridge University Press (2006). 12, 16Google Scholar
Baker, I.N., Multiply connected domain of normality in iteration theory, Math. Z. 81 (1963), 206–214. 12Google Scholar
Baker, I.N., The domains of normality of an entire function, Ann. Acad. Sci. Fenn. Series A. I. Mathematica 1 (1975), 277–283. 14.4CrossRefGoogle Scholar
Baker, I.N., Wandering domains in the iteration of entire functions, Proc. Lond. Math. Soc. (3) (1984), 563–576. 14.4, 23.2Google Scholar
Baker, I.N., Kotus, J., Lü, Y., Iterates of meromorphic functions I, Ergod. Theory Dyn. Syst. 11 (1991), 241–248. 12, 12, 13Google Scholar
Baker, I.N., Kotus, J., Lü, Y., Iterates of meromorphic functions II: Examples of wandering domains, J. Lond. Math. Soc. 42 (1990), 267–278. 14.4, 23.2Google Scholar
Baker, I.N., Kotus, J., Lü, Y., Iterates of meromorphic functions III: Preperi-odic domains, Ergod. Theory Dyn. Syst. 11 (1991), 603–618. 14.3Google Scholar
Baker, I.N., Kotus, J., Lü, Y., Iterates of meromorphic functions IV: Critically finite functions, Results Math. 22 (1992), 651–656. 12, 12, 13, 14.4, 23.2CrossRefGoogle Scholar
Barański, K., Hausdorff dimension and measures on Julia sets of some meromorphic maps, Funda. Math. 147 (1995), 239–260. 12Google Scholar
Barański, K., Fagella, N., Jarque, X., Karpińska, B., On the connectivity of the Julia sets of meromorphic functions, Invent. Math. 198 (2014), 591–636. 14.2CrossRefGoogle Scholar
Barański, K., Karpińska, B., Zdunik, A., Bowen’s formula for meromorphic functions, Ergod. Theory Dyn. Syst. 32:4 (2012), 1165–1189. 10, 17.6, 20Google Scholar
Beardon, A.F., Iteration of Rational Maps, Graduate Texts in Mathematics, vol. 132, Springer-Verlag (1991). 8.6, 13, 13.2Google Scholar
Bergweiler, W., Iteration of meromorphic functions, Bull. New Ser. Am. Math. Soc. 29:2 (1993), 151–188. 12, 12, 13, 13.2.3Google Scholar
Bergweiler, W., Comments and Corrections to “Iteration of meromorphic functions”, https://analysis.math.uni-kiel.de/bergweiler/papers/comments.pdf 13.2.3Google Scholar
Bergweiler, W., Kotus, J., On the Hausdorff dimension of the escaping set of certain meromorphic functions, Trans. Am. Math. Soc., 364 (2012), 5369–5394. 17.7Google Scholar
Bojarski, B., Homeomorphic solutions of Beltrami systems, Dokl. Akad. Nauk SSSR (NS) 102 (1955), 661–664. 23.2, 23.2, 23.2Google Scholar
Bolsch, A., Iteration of meromorphic functions with countably many essential singularities, Dissertation, Berlin (1997). 13.2.3Google Scholar
Bolsch, A., Periodic Fatou components of meromorphic functions, Bull. Lond. Math. Soc. 31 (1999), 543–555. 13.2.3Google Scholar
Bowen, R., Hausdorff dimension of quasi-circles, Publ. Math. IHES 50 (1980), 11–25. 9.5, 11.5, 21Google Scholar
Carleson, L., Gamelin, T.W., Complex Dynamics, Tracts in Mathematics, Springer-Verlag (1993). 13, 13.2Google Scholar
Carleson, L., Jones, P.W., Yoccoz, J.C., Julia and John, Bol. Soc. Bras. Mat./Bull. Braz. Math. Soc. 25 (1994), 1–30. 12, 18Google Scholar
Chen, H., Gauthier, P.M., On Bloch’s constant, J. Anal. Math. 69 (1996), 275–291. 23.2Google Scholar
Conway, J.B., Functions of One Complex Variable, Graduate Texts in Mathematics, vols. I and II, Springer-Verlag (1984). 23.2Google Scholar
Cremer, H., Über die Schrödersche Funktionalgleichung and das Schwarzsche Eckenabbildunsproblem, Ber. Verh. S¨achs. Akad. Wiss. Leipzig, Math-Phys. Kl. 84 (1932), 291–324. 13.2Google Scholar
Denker, M., Mauldin, R.D., Nitecki, Z., Urbański, M., Conformal measures for rational functions revisited, Funda. Math. 157 (1998), 161–173. 10.3, 17.5Google Scholar
Denker, M., Urbański, M., Hausdorff and conformal measures on Julia sets with a rationally indifferent periodic point, J. Lond. Math. Soc. 43 (1991), 107–118. 1.3, 10, 17.6, 20, 22.1, 22.3Google Scholar
Denker, M., Urbański, M., Absolutely continuous invariant measures for expansive rational maps with rationally indifferent periodic points, Forum Math. 3 (1991), 561–579. 22.1, 22.3Google Scholar
Denker, M., Urbański, M., Sullivan’s conformal measures for rational maps of the Riemann sphere, Nonlinearity 4 (1991), 365–384. 10, 17.6, 17.6, 20, 22.4Google Scholar
Denker, M., Urbański, M., Hausdorff measures on Julia sets of subexpanding rational maps, Israel J. Math. 76 (1991), 193–214. 12Google Scholar
Denker, M., Urbański, M., Geometric measures for parabolic rational maps, Ergod. Theory Dyn. Syst. 12 (1992), 53–66. 12, 12, 10, 15.3, 17.6, 20, 21, 22.3Google Scholar
Denker, M., Urbański, M., The capacity of parabolic Julia sets, Math. Z. 211 (1992), 73–86. 10, 15.3, 17.6, 20Google Scholar
DuVal, P., Elliptic Functions and Elliptic Curves, Cambridge University Press (1973). 12, 16, 16.6CrossRefGoogle Scholar
Eremenko, A., Lyubich, M., Iterates of entire functions, Soviet Math. Dokl. 30 (1984), 592–594. 14.4Google Scholar
Eremenko, A., Lyubich, M., Dynamical properties of some classes of entire functions, Ann. Inst. Fourier, 42 (1992), 989–1020. 12, 14.4, 14.4CrossRefGoogle Scholar
Fatou, P., Sur les équations fonctionelles, Bull. Soc. Math. France 47 (1919), 161–271. 12, 14.4, 23.2Google Scholar
Fatou, P., Sur les équations fonctionelles transcendantes, Bull. Soc. Math. France 48 (1920), 208–314. 12, 13.2, 14.4, 23.2Google Scholar
Fatou, P., Sur l’itération des fonctions transcendantes entèries, Acta Math. 47 (1926), 337–370. 12, 14.3Google Scholar
Galazka, P., Kotus, J., Hausdorff dimension of sets of escaping points and escaping parameters for elliptic functions, Proc. Edinburgh Math. Soc. 59 (2016), 671–690. 17.3, 17.7Google Scholar
Galazka, P., Kotus, J., Escaping points and escaping parameters for singly periodic meromorphic maps: Hausdorff dimensions outlook, Complex Var. Elliptic Equ. 63 (2018), 547–568. 17.7Google Scholar
Goldberg, L., Keen, L., A finiteness theorem for a dynamical class of entire functions, Ergod. Theory Dyn. Syst. 6 (1986), 183–192. 14.4Google Scholar
Graczyk, J., Kotus, J., Światek, G., Non-recurrent meromorphic functions, Fund. Math. 182 (2004), 269–281. 18Google Scholar
Hatcher, A., Algebraic Topology, Cambridge University Press (2002). 8.1.1, 8.2, 13.3.2Google Scholar
Hawkins, J., Koss, L., Ergodic properties and Julia sets of Weierstrass elliptic functions, Monatsh. Math. 137 (2002), 273–301. 12, 12, 19, 19.5, 19.6, 19.7.2Google Scholar
Hawkins, J., Koss, L., Parametrized dynamics of the Weierstrass elliptic functions, Conf. Geom. Dynam. 8 (2004), 1–35. 12, 19, 19.4, 19.5.2, 19.7Google Scholar
Hawkins, J., Koss, L., Connectivity properties of Julia sets of Weierstrass elliptic functions, Topol. Appl. 152 (2005), 107–137. 12, 19CrossRefGoogle Scholar
Hawkins, J., Koss, L., Kotus, J., Elliptic functions critical orbits approaching infinity, J. Differ. Equ. Appl. 16 (2010), 613–630. 12, 19, 19.7, 19.7, 19.8.2, 19.8Google Scholar
Hawkins, J., Look, D., Locally Sierpiński Julia sets of Weierstrass elliptic functions, Int. J. Bifurcat. Chaos, 16:5 (2006), 1505–1520. 12, 19Google Scholar
Heins, M., Asymptotic spots of entire and meromorphic functions, Ann. Math. 66 (1957), 430–439. 13.2.3Google Scholar
Herring, M., Mapping properties of Fatou components, Ann. Acad. Sci. Fenn. Math. 23 (1998), 263–274. 13.2.3Google Scholar
Iversen, F., Recherches sur les fonctions inverses des fonctions mero-morphés, Thesis, Helsingforse (1914). 13.3Google Scholar
Jones, G., Singerman, D., Complex Functions: An Algebraic and Geometric Viewpoint, Cambridge University Press (1997). 12, 16, 16.1, 16.5, 23.2, 23.2, A.0.28Google Scholar
Julia, G., Mémoire sur l’iteration des fonctions rationnelles, J. Math. Pures Appl. 8 (1918), 47–245. 12Google Scholar
Kisaka, M., Some conditions for semi-hyperbolicity of entire functions and their applications, in Imayoshi, Y., Komori, Y., Nishio, M., Sakan, K. (eds.), Complex Analysis and its Applications, OCAMI Studies, vol. 2, Osaka Municipal Universities Press (2008), 241–247. 18Google Scholar
Kotus, J., The domains of normality of holomorphic self-map of ℂ*, Ann. Acad. Sci. Fenn. Series A. I. Mathematica 15 (1990), 329–340. 14.4, 23.2Google Scholar
Kotus, J., On the Hausdorff dimension of Julia sets of meromorphic functions. II, Bull. Soc. Math. Fr., 128 (1995), 33–46. 12, 17.3Google Scholar
Kotus, J., Światek, G., Invariant measures for meromorphic Misiurewicz maps, Math. Proc. Camb. Philos. Soc. 145 (2008), 685–697. 22.5Google Scholar
Kotus, J., Urbański, M., Conformal, geometric and invariant measures for transcendental expanding functions, Math. Ann. 324 (2002), 619–656. 12Google Scholar
Kotus, J., Urbański, M., Existence of invariant measures for transcendental subexpanding functions. Math. Z. 243 (2003) 25–36. 2.4, 10, 17.6, 20Google Scholar
Kotus, J., Urbański, M., Hausdorff dimension and Hausdorff measures of elliptic functions, Bull. Lond. Math. Soc. 35 (2003), 269–275. 12, 12, 17, 17.3Google Scholar
Kotus, J., Urbański, M., Geometry and ergodic theory of non-recurrent elliptic functions, J. Anal. Math. 93 (2004) 35–102. 12, 12, 18, 18.1, 18.2, 20.2, 20.3Google Scholar
Kotus, J., Urbański, M., The dynamics and geometry of the Fatou functions, Discrete Contin. Dyn. Syst. 13 (2005), 291–338. 14.3Google Scholar
Kotus, J., Urbański, M., Fractal measures and ergodic theory of transcendental meromorphic functions, in Rippon, P.J., Stallard, G.M. (eds.), Transcendental Dynamics and Complex Analysis London Mathematical Society Lecture Notes Series, vol. 348, Cambridge University Press (2010), 251–316. 17.6, 22.4Google Scholar
Lang, S., Elliptic Functions, Graduate Texts in Mathematics, vol. 112, 2nd ed., Springer (1987). 12, 16Google Scholar
Ljubich, M., Dynamics of rational transforms: the topological picture, Russ. Math. Surv., 41:4 (1986), 43–117. 10.3, 17.5Google Scholar
Lyubich, M., The measurable dynamics of the exponential, Siberian J. Math. 28 (1987), 111–127. 12Google Scholar
Mañé, R., On a theorem of Fatou, Bol. Soc. Bras. Mat. 24 (1993), 1–11. 12, 18, 18.1, 18.1Google Scholar
Mauldin, R.D., Przytycki, F., Urbański, M., Rigidity of conformal iterated function systems, Compos. Math. 129 (2001), 273–299. 12, 11, 22.2, 23Google Scholar
Mauldin, R.D., Urbański, M., Dimensions and measures in infinite iterated function systems, Proc. Lond. Math. Soc. 73:3 (1996), 105–154. 12, 10, 11, 11.3.2, 11.5, 11.5, 11.9, 17.6, 20Google Scholar
Mauldin, R.D., Urbański, M., Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets, Cambridge Tracts in Mathematics, Cambridge University Press (2003). 12, 4.2, 10, 11, 11.3.2, 11.3, 11.4, 11.5, 11.5, 11.6, 11.6, 11.9, 11.9, 17.6, 20, 22.2Google Scholar
Mauldin, R.D., Urbański, M., Gibbs states on the symbolic space over an infinite alphabet, Israel J. Math. 125 (2001), 93–130. 12, 11, 11.6Google Scholar
Mayer, V., Skorulski, B., Urbański, M., Random Distance Expanding Mappings, Thermodynamic Formalism, Gibbs Measures, and Fractal Geometry, Lecture Notes in Mathematics, vol. 2036, Springer (2011). 10, 17.6, 20Google Scholar
Mayer, V., Urbański, M., Gibbs and equilibrium measures for elliptic functions, Mathematische Zeitschrift 250 (2005), 657–683. 12Google Scholar
Mayer, V., Urbański, M., Fractal measures for meromorphic functions of finite order, Dyn. Syst. 22 (2007), 169–178. 21Google Scholar
Mayer, V., Urbański, M., Geometric thermodynamical formalism and real analyticity for meromorphic functions of finite order, Ergod. Theory Dyn. Syst. 28 (2008), 915–946. 12, 10, 17.6, 20, 22.1Google Scholar
Mayer, V., Urbański, M., Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of Finite Order, Memoirs of the American Mathematical Society, vol. 203, no. 954, American Mathematical Society (2010). 12, 10, 17.6, 20, 22.1Google Scholar
Mayer, V., Urbański, M., Thermodynamical formalism for entire functions and integral means spectrum of asymptotic tracts, Trans. AMS 373 (2020), 7669–7711. 12Google Scholar
Mayer, V., Urbański, M., Thermodynamic formalism and geometric applications for transcendental meromorphic and entire functions, in Pollicott, M., Vaienti, S. (eds.), Thermodynamic Formalism: CIRM Jean-Morlet Chair, Fall 2019, Springer (2021), 99–139. 12Google Scholar
Mayer, V., Urbański, M., The exact value of Hausdorff dimension of escaping sets of class B meromorphic functions, Geom. Funct. Anal. 32 (2022), 53–80. 17.7Google Scholar
McMullen, C., Area and Hausdorff dimension of Julia sets of entire functions, Trans. AMS 300 (1987), 329–342. 1.7, 1.7, 17.7Google Scholar
McMullen, C., Hausdorff dimension and conformal dynamics II: Geometrically finite rational maps, Comment. Math. Helv. 75 (2000), 535–593. 10.3, 17.5Google Scholar
Milne-Tomson, L., Jacobian Elliptic Functions Tables, Dover Publications (1950). 5.3, 19.6Google Scholar
Milnor, J., Dynamics in One Complex Variable: Introductory Lectures, Vieweg Verlag (2000). 13, 13.2Google Scholar
Okuyama, Y., Linearization problem on structurally finite entire functions, Kodai Math. J. 28 (2005), 347–358. 18Google Scholar
Patterson, S.J., The limit set of a Fuchsian group, Acta Math. 136 (1976), 241–273. 10, 10.1.1, 17.6, 20Google Scholar
Patterson, S.J., Lectures on measures on limit sets of Kleinian groups, in Epstein, D.B.A. (ed.), Analytical and Geometric Aspects of Hyperbolic Space, London Mathematical Society, Lecture Note Series, vol. 111, Cambridge University Press (1987). 10, 10.1.1, 17.6, 20Google Scholar
Przytycki, F., Iterations of holomorphic Collet–Eckmann maps: conformal and invariant measures, Trans. Am. Math. Soc. 350:2 (1998), 717–742. 18.1Google Scholar
Przytycki, F., Rivera-Letelier, J., Statistical properties of topological Collet–Eckmann maps, Ann. Sci. Éc. Norm. Supér. 40 (2007), 135–178. 12, 12, 22.4, 22.5.1Google Scholar
Przytycki, F., Urbański, M., Rigidity of tame rational functions, Bull. Pol. Acad. Sci. Math. 47:2 (1999), 163–182. 12, 23Google Scholar
Przytycki, F., Urbański, M., Conformal Fractals: Ergodic Theory Methods, London Mathematical Society Lecture Notes Series, vol. 371, Cambridge University Press (2010). 12, 1.5, 7, 9.2, 9.3, 23Google Scholar
Rempe, L., van Strien, S., Absence of line fields and Mane’s theorem for non-recurrent transcendental functions, Trans. AMS 363 (2011), 203–228. 18Google Scholar
Rippon, P., Stallard, G., Iteration of a class of hyperbolic meromorphic functions, Proc. Am. Math. Soc. 127 (1999), 3251–3258. 14.4Google Scholar
Rocha, M.M., Herman rings of elliptic functions, Arnold Math. J., 6 (2020), 551–570. 17.2Google Scholar
Shishikura, M., Lei, T., An alternative proof of Mañé’s theorem on non-expanding Julia sets, in Lei, T. (ed.), The Mandelbrot Set, Theme and Variations, London Mathematical Lecture Note Series, vol. 274, Cambridge University Press (2000), 265–279. 18Google Scholar
Stallard, G., Entire functions with Julia sets of zero measure, Math. Proc. Camb. Philos. Soc. 108 (1990), 551–557. 12Google Scholar
Stallard, G., The Hausdorff dimension of Julia sets of entire functions, Ergod. Theory Dyn. Syst. 11 (1991), 769–777. 12Google Scholar
Steinmetz, N., Rational Iteration, De Gruyter Studies in Mathematics, Reprint 2011, De Gruyter (1993). 13, 13.2Google Scholar
Stratmann, B., Urbański, M., Real analyticity of topological pressure for parabolically semihyperbolic generalized polynomial-like maps, Indag. Mathem. 14 (2003), 119–134. 22.7Google Scholar
Stratmann, B., Urbański, M., Metrical diophantine analysis for tame parabolic iterated function systems, Pacific J. Math. 216 (2004), 361–392. 22.7Google Scholar
Sullivan, D., Quasiconformal homeomorphisms and dynamics I. Solution of the Fatou–Julia problem on wandering domains, Ann. Math. 122 (1985), 401–418. 12, 14.4, 23.2Google Scholar
Sullivan, D., Seminar on conformal and hyperbolic geometry, Institut des Hautes Études Scientifiques, preprint (1982). 10, 10.1.1, 17.6, 20Google Scholar
Sullivan, D., Conformal dynamical systems, in Palis, J. (ed.), Geometric Dynamics, Lecture Notes in Mathematics, vol. 1007, Springer Verlag (1981), 725–752.Google Scholar
Sullivan, D., Quasiconformal homeomorphisms in dynamics, topology, and geometry, Proceedings of the International Congress of Mathematicians, Berkeley, American Mathematical Society (1986), 1216–1228. 12, 10, 17.6, 20, 23Google Scholar
Sullivan, D., The density at infinity of a discrete group, Inst. Hautes Études Sci. Pub. Math. 50 (1979), 171–202. 10, 10.1.1, 17.6, 20Google Scholar
Sullivan, D., Entropy, Hausdorff measures old and new, and the limit set of a geometrically finite Kleinian groups, Acta Math. 153 (1984), 259–277.Google Scholar
Sullivan, D., Disjoint spheres, approximation by imaginary quadratic numbers and the logarithmic law for geodesics, Acta Math. 149 (1982), 215–237. 10, 10.1.1, 17.6, 20Google Scholar
Sumi, H., Urbański, M., Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups, Discrete Contin. Dyn. Syst. 30 (2011), 313–363. 12, 2.4, 23Google Scholar
Töpfer, H., Komplexe Iterationsindizes ganzerund rationaler Funktionen, Math. Ann. 121 (1949), 191–222. 13.2Google Scholar
Urbański, M., On some aspects of fractal dimensions in higher dimensional dynamics, in Proceedings of the Workshop: Problems on Higher Dimensional Complex Dynamics, vol. 3, Gottingensis (1995), 18–25. 10.3, 17.5Google Scholar
Urbański, M., Rational functions with no recurrent critical points, Ergod. Theory Dyn. Syst. 14 (1994), 391–414. 12, 12, 8.4, 10.4, 18, 21Google Scholar
Urbański, M., Geometry and ergodic theory of conformal non–recurrent dynamics, Ergod. Theory Dyn. Syst. 17 (1997), 1449–1476. 12, 12, 5.4, 18, 22.1, 22.3Google Scholar
Urbański, M., Zdunik, A., The finer geometry and dynamics of exponential family, Mich. Math. J. 51 (2003), 227–250. 12, 10, 10.3, 17.5, 17.6, 20, 21Google Scholar
Urbański, M., Zdunik, A., Real analyticity of Hausdorff dimension of finer Julia sets of exponential family, Ergod. Theory Dyn. Syst. 24 (2004), 279–315. 12, 10, 17.6, 20, 22.1Google Scholar
Wittich, H., Neuere Üntersuchungen Uber eindeutige analytische Funktio-nen, Springer-Verlag (1955). 14.4Google Scholar
Young, L.-S., Recurrence times and rates of mixing, J. Math. 110 (1999), 153–188. 12, 4, 4.2, 4.2, 4.2Google Scholar