Hyperbolic dimension and radial Julia sets of transcendental functions-Reference-Cited by-同舟云学术

Hyperbolic dimension and radial Julia sets of transcendental functions

Published:2008-11-03 Issue:4 Volume:137 Page:1411-1420
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Rempe Lasse

Abstract

We survey the definition of the radial Julia set J r ( f ) J_r(f) of a meromorphic function (in fact, more generally, any Ahlfors islands map), and give a simple proof that the Hausdorff dimension of J r ( f ) J_r(f) and the hyperbolic dimension dim hyp ⁡ ( f ) \dim _{\operatorname {hyp}}(f) always coincide.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2009-137-04/S0002-9939-08-09650-0/S0002-9939-08-09650-0.pdf

Reference28 articles.

1. Hausdorff dimension and conformal measures of Feigenbaum Julia sets;Avila, Artur;J. Amer. Math. Soc.,2008

2. Dynamics of functions meromorphic outside a small set;Baker, I. N.;Ergodic Theory Dynam. Systems,2001

3. [BKZ] Krzysztof Barański, Boguslawa Karpińska, and Anna Zdunik, Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts, preprint, 2007, arXiv.org/abs/0711.2672v1.

4. Exceptional values and the MacLane class 𝒜;Barth, Karl F.,2006

5. Extensions of a theorem of Valiron;Barth, Karl F.;Bull. London Math. Soc.,2006

Cited by 23 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Perturbations of exponential maps: Non-recurrent dynamics;Journal d'Analyse Mathématique;2024-09-12

2. The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class;Mathematische Zeitschrift;2022-09-21

3. The failure of Ruelle's property for entire functions;Advances in Mathematics;2021-06

4. Random non-hyperbolic exponential maps;Journal d'Analyse Mathématique;2021-06

5. Non-escaping points of Zorich maps;Israel Journal of Mathematics;2021-05-07