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Rational maps whose Fatou components are Jordan domains

Published online by Cambridge University Press:  14 October 2010

Kevin M. Pilgrim
Kevin M. Pilgrim
Affiliation:
Mathematics Department, White Hall, Cornell University, Ithaca, NY 14853, USA, (e-mail: [email protected])
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Abstract

We prove: If f(z) is a critically finite rational map which has exactly two critical points and which is not conjugate to a polynomial, then the boundary of every Fatou component of f is a Jordan curve. If f(z) is a hyperbolic critically finite rational map all of whose postcritical points are periodic, then there exists a cycle of Fatou components whose boundaries are Jordan curves. We give examples of critically finite hyperbolic rational maps f with a Fatou component ω satisfying f(ω) = ω and f|∂ω not topologically conjugate to the dynamics of any polynomial on its Julia set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 6 , December 1996 , pp. 1323 - 1343
Copyright
Copyright © Cambridge University Press 1996

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