Porosity of Collet–Eckmann Julia sets

Feliks Przytycki; Steffen Rohde

Fundamenta Mathematicae (1998)

  • Volume: 155, Issue: 2, page 189-199
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Przytycki, Feliks, and Rohde, Steffen. "Porosity of Collet–Eckmann Julia sets." Fundamenta Mathematicae 155.2 (1998): 189-199. <http://eudml.org/doc/212251>.

@article{Przytycki1998,
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.},
author = {Przytycki, Feliks, Rohde, Steffen},
journal = {Fundamenta Mathematicae},
keywords = {Hölder domain; shrinking neighborhoods; Collet-Eckmann condition; Julia set; rational map; box dimension; porosity},
language = {eng},
number = {2},
pages = {189-199},
title = {Porosity of Collet–Eckmann Julia sets},
url = {http://eudml.org/doc/212251},
volume = {155},
year = {1998},
}

TY - JOUR
AU - Przytycki, Feliks
AU - Rohde, Steffen
TI - Porosity of Collet–Eckmann Julia sets
JO - Fundamenta Mathematicae
PY - 1998
VL - 155
IS - 2
SP - 189
EP - 199
AB - 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.
LA - eng
KW - Hölder domain; shrinking neighborhoods; Collet-Eckmann condition; Julia set; rational map; box dimension; porosity
UR - http://eudml.org/doc/212251
ER -

References

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