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ArticleOriginal scientific text

Title

Porosity of Collet–Eckmann Julia sets

Authors 1, 2

Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
  2. Department of Mathematics, TU Berlin, Strasse d. 17. Juni 136, 10623 Berlin, Germany

Abstract

We prove that the Julia set of a rational map of the Riemann sphere satisfying the Collet-Eckmann condition and having no parabolic periodic point is mean porous, if it is not the whole sphere. It follows that the Minkowski dimension of the Julia set is less than 2.

Bibliography

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Fundamenta Mathematicae
1998/155/2
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Pages:
189-199
Main language of publication
English
Received
1997-05-08
Accepted
1997-06-25
Published
1998
Exact and natural sciences