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Semiconjugacies between the Julia sets of geometrically finite rational maps

Published online by Cambridge University Press:  01 August 2003

TOMOKI KAWAHIRA
TOMOKI KAWAHIRA
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan (e-mail: kawahira@kusm.kyoto-u.ac.jp)
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Abstract

A rational map f is called geometrically finite if every critical point contained in its Julia set is eventually periodic. If a perturbation of f into another geometrically finite rational map is horocyclic and preserves the critical orbit relations with respect to the Julia set of f, then we can construct a semiconjugacy or a topological conjugacy between their dynamics on the Julia sets.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 4 , August 2003 , pp. 1125 - 1152
Copyright
2003 Cambridge University Press

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