The solar Julia sets of basic quadratic Cremer polynomials

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 connecte...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2010-02, Vol.30 (1), p.51-65
Main Authors: BLOKH, A., BUFF, X., CHÉRITAT, A., OVERSTEEGEN, L.
Format: Article
Language:English
Subjects:
Dynamical Systems
General Topology
Mathematics
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Summary: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385708000990