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Hubbard forests

Published online by Cambridge University Press:  08 November 2011

ALFREDO POIRIER
ALFREDO POIRIER*
Affiliation:
Departmento de Ciencias, Sección Matemáticas, Pontificia Universidad Católica del Perú, Apartado 1761, Lima 100, Perú (email: apoirie@pucp.edu.pe)
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Abstract

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The theory of Hubbard trees provides an effective classification of nonlinear postcritically finite polynomial maps in ℂ. This note extends the classification to maps from a finite union of copies of ℂ to itself. Holomorphic proper maps on a finite union of copies of ℂ which are postcritically finite and nowhere linear can be characterized by a ‘forest’ made up of one tree for each copy of the set of complex numbers.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 1 , February 2013 , pp. 303 - 317
Copyright
Copyright © Cambridge University Press 2011

References

[1]Douady, A.. Descriptions of compact sets in ℂ. Topological Methods in Modern Mathematics: A Symposium in Honor of John Milnor’s Sixtieth Birthday. Publish or Perish, Inc., Houston, 1993, pp. 429–465.Google Scholar
[2]Douady, A. and Hubbard, J.. Étude dynamique des polynômes complexes, I, II. Publ. Math. Orsay (1984–1985).Google Scholar
[3]Milnor, J.. Dynamics in One Complex Variable: Introductory Lectures. Vieweg, Wiesbaden, 2000.CrossRefGoogle Scholar
[4]Nakane, S. and Schleicher, D.. On multicorns and unicorns I: antiholomorphic dynamics, hyperbolic components and real cubic polynomials. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13(10) (2003), 2825–2844.CrossRefGoogle Scholar
[5]Poirier, A.. Hubbard trees. Fund. Math. 208(3) (2010), 193–248.CrossRefGoogle Scholar
[6]Sullivan, D.. Quasiconformal homeomorphisms and dynamics I: solution to the Fatou–Julia problem on wandering domains. Ann. of Math. (2) 122 (1985), 401–418.CrossRefGoogle Scholar