Journal of Modern Dynamics (JMD)

The Julia set of a post-critically finite endomorphism of $\mathbb{PC}^2$
Pages: 327 - 375, Issue 3, July 2012

doi:10.3934/jmd.2012.6.327      Abstract        References        Full text (999.4K)           Related Articles

Volodymyr Nekrashevych - Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, United States (email)

1 Laurent Bartholdi and Volodymyr V. Nekrashevych, Thurston equivalence of topological polynomials, Acta Math., 197 (2006), 1-51.       
2 Joan S. Birman, "Braids, Links, and Mapping Class Groups," Annals of Mathematics Studies, 82, Princeton University Press, Princeton, N.J., 1974.       
3 Adrien Douady and John H. Hubbard, "Étude Dynamiques des Polynômes Complexes. (Première Partie)," Publications Mathematiques d'Orsay, 2, Université de Paris-Sud, 1984.
4 Adrien Douady and John H. Hubbard, "Étude Dynamiques des Polynômes Complexes. (Deuxième Partie)," Publications Mathematiques d'Orsay, 4, Université de Paris-Sud, 1985.
5 Adrien Douady and John H. Hubbard, A proof of Thurston's topological characterization of rational functions, Acta Math., 171 (1993), 263-297.       
6 J. E. Fornæss and N. Sibony, Critically finite rational maps on $\mathbbP^2$, in "The Madison Symposium on Complex Analysis" (Madison, WI, 1991), Contemp. Math., 137, Amer. Math. Soc., Providence, RI, (1992), 245-260.       
7 Yutaka Ishii and John Smillie, Homotopy shadowing, Amer. J. Math., 132 (2010), 987-1029.       
8 S. Koch, "Teichmüller Theory and Endomorphisms of $\mathbbP^n$," Ph.D. thesis, Université de Provence, 2007.
9 John Milnor, Pasting together Julia sets: A worked out example of mating, Experiment. Math., 13 (2004), 55-92.       
10 Volodymyr Nekrashevych, "Self-Similar Groups," Mathematical Surveys and Monographs, 117, Amer. Math. Soc., Providence, RI, 2005.       
11 Volodymyr Nekrashevych, A minimal Cantor set in the space of 3-generated groups, Geometriae Dedicata, 124 (2007), 153-190.       
12 Volodymyr Nekrashevych, Combinatorial models of expanding dynamical systems, preprint, arXiv:0810.4936, 2008.
13 Volodymyr Nekrashevych, Symbolic dynamics and self-similar groups, in "Holomorphic Dynamics and Renormalization" (eds. Mikhail Lyubich and Michael Yampolsky), Fields Institute Communications, 53, Amer. Math. Soc., Providence, RI, (2008), 25-73.       
14 Volodymyr Nekrashevych. Combinatorics of polynomial iterations. In D. Schleicher, editor, Complex Dynamics - Families and Friends, pages 169-214. A K Peters, 2009.       
15 Volodymyr Nekrashevych, A group of non-uniform exponential growth locally isomorphic to $IMG$$(z^2+i)$, Transactions of the AMS, 362 (2010), 389-398.       
16 Alfredo Poirier, The classification of postcritically finite polynomials II: Hubbard trees, Stony Brook IMS preprint, 1993.
17 John S. Wilson, On exponential growth and uniform exponential growth for groups, Inventiones Mathematicae, 155 (2004), 287-303.       

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