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Cambridge University Press
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February 2014
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Since its introduction in the early 1980s quasiconformal surgery has become a major tool in the development of the theory of holomorphic dynamics, and it is essential background knowledge for any researcher in the field. In this comprehensive introduction the authors begin with the foundations and a general description of surgery techniques before turning their attention to a wide variety of applications. They demonstrate the different types of surgeries that lie behind many important results in holomorphic dynamics, dealing in particular with Julia sets and the Mandelbrot set. Two of these surgeries go beyond the classical realm of quasiconformal surgery and use trans-quasiconformal surgery. Another deals with holomorphic correspondences, a natural generalization of holomorphic maps. The book is ideal for graduate students and researchers requiring a self-contained text including a variety of applications. It particularly emphasises the geometrical ideas behind the proofs, with many helpful illustrations seldom found in the literature.


'This worthwhile book, written by two of the main experts in this field with some contributions from some well-known researchers, gives a comprehensive introduction to the subject, from the foundations of the theory up to several important and representative applications … All in all, this book is a very welcome addition to the literature, and an excellent entrance point to the theory for any researcher interested in this subject.'

Marco Abate Source: Zentralblatt MATH

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[Ah1] L., Ahlfors (1964) Finitely generated Kleinian groups, Amer. J. Math. 86, 413–129.
[Ah2] L., Ahlfors (1966) Lectures on Quasiconformal Mappings. Van Nostrand.
[Ah3] L., Ahlfors (1973) Conformal Invariants: Topics in Geometric Function Theory. McGraw-Hill.
[Ah4] L., Ahlfors (1978) Complex Analysis. An Introduction to the Theory of Analytic Functions ofOne Complex Variable, 3rd edition. McGraw-Hill.
[Ah5] L., Ahlfors (2006) Lectures on Quasiconformal Mappings, 2nd edition. Vol. 38, American Mathematical Society.
[AB] L., Ahlfors and L., Bers (1960) Riemann mapping's theorem for variable metrics, Annals of Math. 72, 385–404.
[An] J. W., Anderson (1998) A brief survey of the deformation theory of Kleinian groups, in The Epstein Birthday Schrift, eds I., Rivin, C., Rourke and C., Series. Geometry and Topology Monographs 1, pp. 23–49. Mathematics Institute, University of Warwick.
[AMa] J. W., Anderson and B., Maskit (1996) On the local connectivity of limit sets of Kleinian groups, Complex Variables Theory Appl. 31, 177–183.
[AIM] K., Astala, T., Iwaniec and G., Marten (2009) Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane. Princeton University Press.
[AM] K., Astala and G. J., Martin (2001) Holomorphic motions, in Papers on Analysis, pp. 27–40. Rep. Univ. Jyvaskyla Dep. Math. Stat., 83.
[Ar1] V. I., Arnol'd (1965) Small denominators. I: Mappings of the circumference onto itself, Am. Math. Soc., Transl., II. Ser. 46, 213–284; translated from Izv. Akad. Nauk SSSR, Ser. Mat. 25 (1961), 21–86.
[Ar2] V. I., Arnol'd (1983) Geometrical Methods in the Theory of Ordinary Differential Equations. Springer.
[As] K., Astala (1994) Area distortion of quasiconformal mappingsActa Math. 173, 37–60.
[BA] A., Beurling and L., Ahlfors (1956) The boundary correspondence under quasiconformal mappings, Acta Math. 96, 125–142.
[BC] X., Buff and A., Cheritat (2004) Upper bound for the size of quadratic Siegel discs, Invent. Math. 156, 1–24.
[BD] B., Branner and A., Douady (1986) Surgery on ComplexPolynomials, Proceedingsofthe Second International Colloquium on Dynamical Systems, Mexico, pp. 11–72. SpringerVerlag.
[BDH] C., Bodelón, R., Devaney, M., Hayes, G., Gareth, L., Goldberg and J. H., Hubbard (2000) Dynamical convergence of polynomials to the exponential, J. Differ. Eq. Appl. 6, 275–307.
[Be1] L., Bers (1960) Simultaneous uniformization, Bull. Amer. Math. Soc. 66, 95–97.
[Be2] L., Bers (1972) Uniformization, moduli, and Kleinian groups, Bull. Lon. Math. Soc. 4, 257–300.
[Be3] L., Bers (1985) On Sullivan's proof of the finiteness theorem and the eventual periodicity theorem, Amer. J. Math. 109, 833–852.
[Bea] A., Beardon (1991) Iteration of Rational Functions. Springer Verlag.
[Be1] E., Beltrami (1868) Saggio di interpretazione della geometria non euclidia, Giorn Math. 6, 285–315.
[Ber] W., Bergweiler (1993) Iteration of meromorphic functions, Bull. Amer. Math. Soc. 29, 151–188.
[BerE] W., Bergweiler and A., Eremenko (1995) On the singularities of the inverse of a meromorphic function of finite order, Rev. Mat. Iberoamericana 11, 355–373.
[BF1] B., Branner and N., Fagella (1999) Homeomorphisms between limbs of the Mandelbrot set, J. Geom. Anal. 9, 327–390.
[BF2] B., Branner and N., Fagella (2001) Extension of homeomorphisms between limbs of the Mandelbrot set, Conf. Geom. and Dyn. 5, 100–139.
[BFGH] X., Buff, N., Fagella, L., Geyer and C., Henriksen (2005) Herman rings and Arnold disks, J. Lon. Math. Soc. 72, 689–716.
[BH] B., Branner and J. H., Hubbard (1988) The iteration of cubic polynomials. Part I: the global topology of parameter space, Acta Math. 160, 143–206.
[BHai] S., Bullett and P., Haissinsky (2007) Pinching holomorphic correspondences, Conf. Geom. Dyn. 11, 65–89.
[BHar] S., Bullett and W., Harvey (2000) Mating quadratic maps with Kleinian groups via quasiconformal surgery, Electronic Research Announcements of the AMS, 6, 21–30.
[BHe] X., Buff and C., Henriksen (2001) Julia sets in parameter space, Comm. Math. Phys. 220, 333–375.
[Bi1] B., Bielefeld (1989) Changing the order of critical points of polynomials using quasiconformal surgery, PhD thesis, Cornell University
[Bi2] B., Bielefeld (1990) Questions in quasiconformal surgery, 2–8, in Conformal Dynamics Problem List, ed. B., Bielefeld. Stony Brook IMS Preprint 1990/1. Also published in part 2 of Linear and Complex Analysis Problem Book 3 (1994), eds. V. P. Havin and N. Nikolskii. Springer-Verlag.
[B1] P., Blanchard (1984) Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc. 11, 85–141.
[Bo1] B., Bojarski (1955) Homeomorphic solutions of Beltrami systems, Dokl. Akad. Nauk. SSSR 102, 661–664.
[Bo2] B., Bojarski (2010) On the Beltrami equation, once again: 54 years later, Ann. Acad. Sci. Fenn. Math. 35, 5973.
[Bö] L. E., Böttcher (1904) The principal law of convergence of iterates and their applications to analysis (in Russian), Izv. Kazan. Fiz.-Mat. Bsch. 14, 155–234.
[BP1] S., Bullett and C., Penrose (1994) Mating quadratic maps with the modular group, Invent. Math. 115, 483–511.
[BP2] S., Bullett and C., Penrose (2001) Regular and limit sets for holomorphic correspondences, Fund. Math. 167, 111–171.
[BPer] A., Bridy and R., Perez (2005) A count of maximal small copies in multibrot sets, Nonlinearity 18, 1945–1953.
[BR] L., Bers and H. L., Royden (1986) Holomorphic families of injections, Acta Math. 157, 259–286
[Bra1] B., Branner (1989) The Mandelbrot set, Proc. Symp. Applied Math. 39, 75–105.
[Bra2] B., Branner (1993) Cubic polynomials: turning around the connectedness locus, in Topological Methods in Modern Mathematics, eds. L. R., Goldberg and A. V., Philips, pp. 391–427. Publish or Perish, Inc.
[BrHa] M. R., Bridson and A., Haefliger (1999) Metric Spaces of Non-positive Curvature. Springer.
[Bry1] A. D., Bryuno (1965) Convergence of transformations of differential equations to normal forms, Dokl. Akad. Nauk USSR 165, 987–989 (Soviet Math. Dokl., 1536–1538).
[Bu] X., Buff, Personal communication.
[C] S.-S., Chern (1955) An elementary proof of the existence of isothermal parameters on a surface, Proc. Amer. Math. Soc. 6, 771–782.
[CG] L., Carleson and T., Gamelin (1993) Complex Dynamics. Springer Verlag.
[Ch] A., Cheritat (2006) Ghys-like models for Lavaurs and simple entire maps, Conform. Geom. Dyn. 10, 227–256.
[CL] E. F., Collingwood and A. J., Lohwater (1966) The Theory of Cluster Sets. Cambridge University Press.
[Co] J. B., Conway (1995) Functions of One Complex Variable II. Springer Verlag.
[Com] M., Comerford (2013) The Caratheodory topology for multiply connected domains I, Cent. Eur. J. Math. 11, 322–340.
[Cr] H., Cremer (1932) Über die Schrödersche Funktionalgleichung und das Schwarzsche Eckenabbildungsproblem, Ber. Verh. Sachs. Akad. Wiss. Leipzig, Math.-Phys. Kl. 84, 291–324.
[Da] G., David (1988) Solutions de l'équation de Beltrami avec ∥μ∥∞ = 1, Ann. Acad. Sci. Fenn. Ser. A 1 Math. 13, 25–70.
[DB] A., Douady and X., Buff (2000) Le théorème d'integrabilite des structures presque complexes, in The Mandelbrot Set, Theme and Variations, ed. Tan, Lei, pp. 307–324. Cambridge University Press.
[Den] A., Denjoy (1932) Sur les courbes définies par les équations differentieles á lasurface du tore, J. Math. Pure et Appl. 11, série 9, 333–375.
[Dev1] R. L., Devaney (ed.) (1994) Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia sets, Proceedings of Symposia in Applied Matehmatics, Vol. 49. American Mathematical Society.
[Dev2] R. L., Devaney (1989) An Introduction to Chaotic Dynamical Systems, 2nd edition. Addison-Wesley.
[DE] A., Douady and C., Earle (1986) Conformally natural extension of homeomorphisms of the circle, Acta Math. 157, 23–48.
[DF] P., Domínguez and N., Fagella (2004) Existence of Herman rings for transcendental meromorphic functions, Comp. Var. Theory and Appl. 49, 851–870.
[DH1] A., Douady and J. H., Hubbard (1982) Iterations des Polynomes Quadratiques Complexes, C.R. Acad. Sci., Paris, Ser. I 29, 123–126.
[DH2] A., Douady and J. H., Hubbard (19841985) Étude dynamique des polynômes complexes, I, II, Publ. Math. Orsay. English version at
[DH3] A., Douady and J. H., Hubbard (1985) On the dynamics of polynomial-like mappings, Ann. Scient., Ec. Norm. Sup. 4e series, 18, 287–343.
[dFdM] E., de Faria and W., de Melo (1999) Rigidity of critical circle mappings I, J. Eur. Math. Soc. (JEMS) 1, 339–392.
[dMvS] W., de Melo and S., van Strien (1991) One-Dimensional Dynamics. Springer-Verlag.
[Do1] A., Douady (1986) Chirugie sur les applications holomorphes, in Proc. Int. Congr. Math., Berkeley, pp. 724–738.
[Do2] A., Douady (1983) Systèmes dynamiques holomorphes, Astérisque, 105/106, 39–63.
[Do3] A., Douady (1987) Disques de Siegel et anneaux de Herman, Astérisque, 152/153, 151–172.
[DT] R. L., Devaney and F., Tangerman (1986) Dynamics of entire functions near the essential singularity, Erg. Th. Dyn. Syst. 6, 489–503.
[EL1] E. L., Eremenko and M., Lyubich (1990) The dynamics of analytic transformations, Leningrad Math. J. 1, 563–634.
[EL2] E. L., Eremenko and M., Lyubich (1992) Dynamical properties of some classes of entire functions, Ann. Inst. Fourier 42, 989–1020.
[Ep] A. L., Epstein (1993) Towers of finite type complex analytic maps, PhD thesis, CUNY. Available at
[Ep1] A., Epstein, Counterexamples to the quadratic mating conjecture (unpublished manuscript).
[Ep2] A. L., Epstein (1999) Infinitesimal Thurston rigidity and the Fatou–Shishikura inequality, Stony Brook I.M.S. Preprint 1999#1 or arXiv:math./9902158 at
[Ep3] A. L., Epstein (2013) Algebraic dynamics I: Contraction and finiteness principles (in preparation).
[EY] A., Epstein and M., Yampolsky (1999) Geography of the cubic connectedness locus I: Intertwining surgery, Ann. Scient. Ec. Norm. Sup. 32, 151–185.
[Fat] P., Fatou, Sur les equations fonctionnelles, Bull. Soc. Math. Fr. 47 (1919), 161–271; 48(1920), 33–94, 208–304.
[Fau] D., Faught (1992) Local connectivity in a family of cubic polynomials, PhD thesis, Cornell University.
[FK] H., Farkas and I., Kra (1980) Riemann Surfaces. Springer.
[FG] N., Fagella and L., Geyer (2003) Surgery on Herman rings of the complex standard family, Erg. Th. and Dyn. Sys. 23, 493–508.
[FSY] M., Flexor, P., Sentenac and J. C., Yoccoz (eds.) (2000) Geometrie complexe et systemes dynamiques, Astérisque 261.
[Ga] C. F., Gauss (1973) Werke. Band IV, 193–216. Reprint of the 1863 original. Georg Olms Verlag, Hildesheim.
[Ge1] L., Geyer (1995) Iteration of quasiregular mappings in two dimensions (preprint).
[Ge2] L., Geyer (2001) Siegel disks, Herman rings and the Arnold family, Trans. Amer. Math. Soc. 353, 3661–3683.
[Gh] E., Ghys (1984) Transformations holomorphes au voisinage d'une courbe de Jordan, C.R. Acad. Sc. Paris 289, 383–388
[GK] L. R., Goldberg and L., Keen (1986) A finiteness theorem for a dynamical class of entire functions, Erg. Th. and Dyn. Syst. 6, 183–192.
[GM] L., Goldberg and J., Milnor (1993) Fixed points of polynomial maps II, Ann. Scient. Éc. Norm. Sup., 4e série, 26, 51–98.
[Go] G. M., Goluzin (1969) Geometric Theory of Functions of a Complex Variable, Vol. 26. American Mathematical Society.
[GRSY] V., Gutlyanskii, V., Ryazanov, U., Srebro and E., Yakubov (2012) The Beltrami Equation, A Geometric Approach, Developments in Mathematics, Vol. 26, Springer.
[GS] J., Graczyk and G., Swiatek (1997) Generic hyperbolicity in the logistic family, Ann. Math. 146, 1–52.
[Ha1] P., Haïssinsky (2000) Chirurgie croisée, Bull. Soc. Math. de France 128, 599–654
[Ha2] P., Haïssinsky (1998) Chirurgie parabolique, C.R. Acad. Sci. Paris Ser. I Math. 327, 195–198.
[Ha3] P., Haïssinsky (2000) Déformation J-équivalente de polynômes geometriquement finis, Fund. Math. 163, (2), 131–141.
[He1] M., Herman (1979) Sur la conjugaison différentiable des diffeomorphismes du cercle à des rotations, Publ. Math. I. H. E. S. 49, 5–234.
[He2] M., Herman (1986) Conjugaison quasi-symétrique des difféphismes du cercels et applications aux disques singuliers de Siegel (unpublished manuscript).
[He3] M., Herman (1987) Conjugaison quasi-symétrique des homeomorphismes analytiques du cercels à des rotations (unpublished manuscript).
[HP] P. G., Hjorth and C. L., Petersen (eds.) (2006) Dynamics on the Riemann Sphere. European Mathematical Society.
[HT] P., Haïssinsky and Tan, Lei (2004) Convergence of pinching deformations and matings of geometrically finite polynomials, Fund. Math. 181(2), 143–188.
[Hu1] J. H., Hubbard (1992) Local connectivity of Julia sets and bifurcation loci: three theorems of J.-C. Yoccoz, in Topological Methods in Modern Mathematics, pp. 467–511 and 375–378. Publish or Perish, Inc.
[Hu2] J. H., Hubbard (2006) Teichmüller Theory and Applications to Geometry, Topology and Dynamics, Vol. 1. Matrix Editions.
[HY] Xin-Hou, Hua and Chung-Chun, Yang (1998) Dynamics of Transcendental Functions. Gordon and Breach Science Publishers.
[J] G., Julia (1918) Memoire sur l'iteration des fonctions rationnelles, J. Math. Pure Appl. 8, 47–245.
[K] L., Keen (ed.) (2010) Special issue dedicated to Robert L. Devaney on the occasion of his 60th Birthday, J. Diff. Eq. Appl. 16.
[Ke] J. L., Kelley (1975) General Topology. Springer-Verlag.
[Kin] A. Ya., Khinchin (1997) Continued Fractions. Dover Publications.
[Kiw] J., Kiwi (2000) Non-accessible critical points of Cremer polynomials, Erg. Th. Dyn. Syst. 20, 1391–1403.
[Ko] A., Korn (1914) Zwei Anwendungen der Methode der sukzessiven Annaherungen, in Schwarz-Festschr. pp. 215–229.
[Kæ] G., Kænigs (1884) Recherches sur les intégrales de certaines équations fonctionelles, Ann. Sci. École Norm. Sup. Paris 1, supplém., 1–41.
[Kre] E., Kreyszig (1978) Inroductory Functional Analysis with Applications. Wiley.
[Kri] H., Kriete (ed.) (1998) Progress in Holomorphic Dynamics. Longman.
[KSvS] O., Kozlovski, W., Shen and S., van Strien (2007) Density of hyperbolicity in dimension one, Ann. Mat. 166, 145–182.
[KZ] L., Keen and G., Zhang (2009) Bounded-type Siegel disks of a one-dimensional family of entire functions, Erg. Th. and Dyn. Syst. 29, 137–164.
[Lan] S., Lang (1995) Introduction to Diophantine Approximations. Springer-Verlag.
[Lav] P., Lavaurs (1989) Systèmes dynamiques holomorphes: explosion de points périodiques,These, Université de Paris-Sud.
[Lavr] M. A., Lavrentiev (1935) Sur une classe de répresentations continues, Rec. Math. 48, 407–423.
[Lea] L., Leau (1897) Étude sur les equations fonctionelles à une ou plusiérs variables, Ann. Fac. Sci. Toulouse 11, E1–E110.
[Le] O., Lehto (1986) Univalent Functions and Teichmüller Spaces. Springer-Verlag.
[Li] L., Lichtenstein (1916) Zur Theorie der konformen Abbildung nichtanalytischer singu-laritätenfreier Flächenstücke auf ebene Gebiete, Kram. Anz., 192–217.
[LV] O., Lehto and K. I., Virtanen (1973) Quasiconformal Mappings in the Plane. Springer-Verlag.
[Ly] M., Lyubich, Conformal geometry and dynamics of quadratic polynomials (in preparation).
[Mar] A., Marden (2007) Outer Circles. An Introduction to Hyperbolic 3-Manifolds. Cambridge University Press.
[Mas] B., Maskit (1967) A characterization of Schottky groups, J. d'Analyse Mat. 19, 227–230.
[McM] C. T., McMullen, Simultaneous uniformization of Blaschke products (unpublished manuscript).
[McM1] C. T., McMullen (1986) Automorphisms of rational maps, in Holomorphic Functions and Moduli, Vol. I (Berkeley, CA, 1986), pp. 31–60. Math. Sci. Res. Inst. Publ., 10, Springer, 1988.
[McM2] C. T., McMullen (1994) Complex Dynamics and Renormalization. Princeton University Press.
[McM3] C., McMullen (1996) Renormalization and 3-Manifolds which Fiber Over the Circle. Princeton University Press.
[McM4] C. T., McMullen (1998) Self-similarity of Siegel discs and Hausdorff dimension of Julia sets, Acta. Math. 180, 247–292.
[Mi1] J., Milnor (2006) Dynamics in One Complex Variable: Introductory Lectures, 3rd ed., Princeton University Press.
[Mi2] J., Milnor (2004) Pasting together Julia sets, Exp. Math. 13(1), 55–92.
[Mi3] J., Milnor (1992) Remarks on iterated cubic maps, Exp. Math. 1, 5–24.
[Mi4] J., Milnor (2009) On cubic polynomials with periodic critical point, in Complex Dynamics: Families and Friends, p. 257. A.K. Peters.
[Mi5] J., Milnor (2012) Hyperbolic components, in Conformal Dynamics and Hyperbolic Geometry, pp. 183–232. American Mathematical Society.
[MNTU] S., Morosawa, Y., Nishimura, M., Taniguchi and T., Ueda (1999) Holomorphic Dynamics. Cambridge University Press.
[Mo] C. B., Morrey (1938) On the solutions of quasi-linear elliptic partial differential quations, Trans. Amer. Math. Soc. 43, 126–166.
[MS] C., McMullen and D., Sullivan (1998) Quasiconformal homeomorphisms and dynamics III: the Teichmuller space of a rational map. Adv. Math. 135, 351–395.
[MSS] R., Mañé, P., Sad and D., Sullivan (1983) On the dynamics of rational maps, Ann. Scie. École Norm. Sup.(4) 16, 51–98 and 193–217.
[MSW] D., Mumford, C., Series and D., Wright (2002) Indira's Pearls: The Vision of Felix Klein. Cambridge University Press.
[MT] K., Matsuzaki and M., Taniguchi (1998) Hyperbolic Manifolds and Kleinian Groups. Clarendon Press.
[N] V. I., Năishul' (1983) Topological invariants of analytic and area preserving mappings and their application to analytic differential equations in ℂ2 and ℂℙ2, Trans. Moscow Math. Soc. 42, 239–250.
[NZM] I., Niven, H. S., Zuckerman and H. L., Montgomery (1991) An Introduction to the Theory of Numbers, 5th ed. Wiley.
[Pe1] C. L., Petersen (1996) Local connectivity of some Julia sets containing a circle with an irrational rotation, Acta Math. 177, 163–224.
[Pe2] C. L., PetersenThe Herman–Świaa̧tek Theorems with applications, in The Mandelbrot Set, Theme and Variations, ed. Tan, Lei, pp. 211–225. Cambridge University Press.
[Pe3] C. L., Petersen (2004) On holomorphic critical quasi-circle maps, Erg. Th. Dyn. Syst. 24, 1739–1751.
[PeT] C. L., Petersen and Tan, Lei (2006) Branner–Hubbard motions and attracting dynamics, in Dynamics on the Riemann Sphere, eds. P. G., Hjorth and C. L., Petersen, pp. 45–70. European Mathematical Society.
[Pi] G., Piranian (1958) The boundary of a simply connected domain, Bull. Amer. Math. Soc. 64, 45–55.
[PM] R., Perez-Marco (1997) Fixed points and circle maps, Acta Math. 179, 273–294.
[Poi] H., Poincaré (1885) Sur les courbes défines par des équations différentielles, J. Math. Pures et Appl., 4e série, 1, 167–244.
[Pom] Ch., Pommerenke (1992) Boundary Behavior of Conformal Maps. Springer.
[PT1] K., Pilgrim and Tan, Lei (1999) On disc-annulus surgery of rational maps, in Proceedings ofthe International Conference in Honor of Professor Shantao Liao, eds. Y., JiangandL., Wen, pp. 237–250. World Scientific.
[PT2] K., Pilgrim and Tan, Lei (2000) Rational maps with disconnected Julia set, Astérisque 261, 349–384.
[PZ] C. L., Petersen and S., Zakeri (2004) On the Julia set of a typical quadratic polynomial with a Siegel disk, Ann. Math. (2) 159, 1–52.
[R] J., Riedl (2000) Arcs in multibrot sets, locally connected Julia sets and their construction by quasiconformal surgery, PhD thesis, Technische Universität München Zentrum Mathematik.
[Ro] R. C., Robinson (2004) An Introduction to Dynamical Systems. Northwestern University.
[Roh] S., Rohde (1997) Bilipschitz maps and the modulus of rings, Ann. Acad. Sci. Fen. Math. 22, 465–474.
[Rü] H., Rüssman (1967) Über die Iteration analytischer Funcionen (in German), J. Math. Mech 17, 523–532.
[RS] P. J., Rippon and G. M., Stallard (eds.) (2008) Transcendental Dynamics and Complex Analysis. Cambridge University Press.
[Sc] D., Schleicher (ed.) (2009) Complex Dynamics: Families and Friends. A.K. Peters.
[Sh1] M., Shishikura (1987) On the quasiconformal surgery of rational functions, Ann. Sci. Ec. Norm. Sup. 20, 1–29.
[Sh2] M., Shishikura (1998) The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets. Ann. of Math. 147, 225–267.
[Sh3] M., Shishikura (2000) On a theorem of M. Rees for matings of polynomials, in The Mandelbrot Set, Theme and Variations, pp. 289–305. Cambridge University Press.
[Shu] M., Shub (1970) Expanding maps, in Global Analysis, AMS Proc. of Symp. XIV, pp. 273–276. American Mathematical Society.
[Si] C. L., Siegel (1942) Iteration of analytic functions, Ann. of Math. 43, 607–612.
[Sl] Z., Slodkowski (1991) Holomorphic motions and polynomial hulls, Proc. Amer. Math. Soc. 111, 347–355.
[St] N., Steinmetz (1993) Rational Iteration: Complex Analytic Dynamical Systems. Walter de Gruyter.
[Su1] D., Sullivan (1983) Conformal dynamical systems, in Geometric Dynamics (Rio de Janeiro, 1981), pp. 725–752. Springer.
[Su2] D., Sullivan (1985) Quasiconformal homeomorphisms and dynamics. I. Solution of the Fatou-Julia problem on wandering domains. Ann. of Math. 122, 401–418.
[ST] D., Sullivan and W. P., Thurston (1986) Extending holomorphic motions, Acta Math. 157, 243–257.
[Sw1] G., Świa̧tek (1988) Rational rotation numbers for maps of the circle, Comm. Math. Phys. 119, 109–128.
[Sw2] G., Świa̧tek (1998) On critical circle homeomorphisms, Bol. Soc. Bras. Mat. (N. S.), 29, 329–351.
[Ta1] Tan, L. (1992) Matings of quadratic polynomials, Erg. Th. Dyn. Syst. 12, 589–620.
[Ta2] Tan, L. (ed.) (2000) The Mandelbrot Set, Theme and Variations. Cambridge University Press.
[Tu1] P., Tukia (1986) On quasiconformal groups, J. Analyse Math. 46, 318–346.
[Tu2] P., Tukia (1991) Compactness properties of μ-homeomorphisms, Ann. Acad. Sci. Fenn. Ser. A I Math. 16, 47–69.
[TY] Tan, L. and Yin, Y. (1996) Local connectivity of the Julia set for geometrically finite rational maps, Sci. China Ser. A 39, 39–47
[Why] S., Whyburn (1942) Analytic Topology, AMS Coll. Publ. 28.
[Yo1] J.-C., Yoccoz (1988) Linéarisation des germes de difféomorphismes holomorphes de (ℂ, 0), C.R. Acad. Sci. Paris 306, 55–58.
[Yo2] J.-C., Yoccoz (1989) Structure des orbites des homéomorphismes analytiques posedant un point critique (unpublished manuscript).
[Yo3] J.-C., Yoccoz, Conjugaison des diffeomorphismes analytiques du cercle (unpublished manuscript).
[Yo4] J.-C., Yoccoz (1992) An introduction to small divisors problems, in From Number Theory to Physics, pp. 659–679. Springer-Verlag.
[YZ] M., Yampolsky and S., Zakeri (2001) Mating Siegel quadratic polynomials, J. Amer. Math. Soc. 14, 25–78.
[Z1] S., Zakeri (1999) Dynamics of cubic Siegel polynomials, Comm. Math. Phys. 206, 185–233.
[Z2] S., Zakeri (2010) On Siegel disks of a class of entire maps, Duke Math. J. 152, 481–532.
[Zh] G., Zhang (2011) All bounded type Siegel disks of rational maps are quasidisks, Ivent. Math. 185, 421–466.


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