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The solar Julia sets of basic quadratic Cremer polynomials

Published online by Cambridge University Press:  17 March 2009

A. BLOKH ,
X. BUFF ,
A. CHÉRITAT  and
L. OVERSTEEGEN
A. BLOKH
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170, USA (email: ablokh@math.uab.edu, overstee@math.uab.edu)
X. BUFF
Affiliation:
Université de Toulouse; UPS, INSA, UT1, UTM; Institut de Mathématiques de Toulouse; F-31062 Toulouse, France CNRS; Institut de Mathématiques de Toulouse UMR 5219; F-31062, Toulouse, France (email: xavier.buff@math.univ-toulouse.fr, arnaud.cheritat@math.univ-toulouse.fr)
A. CHÉRITAT
Affiliation:
Université de Toulouse; UPS, INSA, UT1, UTM; Institut de Mathématiques de Toulouse; F-31062 Toulouse, France CNRS; Institut de Mathématiques de Toulouse UMR 5219; F-31062, Toulouse, France (email: xavier.buff@math.univ-toulouse.fr, arnaud.cheritat@math.univ-toulouse.fr)
L. OVERSTEEGEN
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170, USA (email: ablokh@math.uab.edu, overstee@math.uab.edu)
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Abstract

In general, little is known about the exact topological structure of Julia sets containing a Cremer point. In this paper we show that there exist quadratic Cremer Julia sets of positive area such that for a full Lebesgue measure set of angles the impressions are degenerate, the Julia set is connected im kleinen at the landing points of these rays, and these points are contained in no other impression.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 1 , February 2010 , pp. 51 - 65
Copyright
Copyright © Cambridge University Press 2009

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