Hyperbolic Dimension of Julia Sets of Meromorphic Maps with Logarithmic Tracts

By Krzysztof Bara'nski, B. Karpinska, A. Zdunik. 2007

53 citations recorded by the source corpus.

We prove that for meromorphic maps with logarithmic tracts (in particular, for transcendental maps in the class , which are entire or meromorphic with a finite number of poles), the Julia set contains a compact invariant hyperbolic Cantor set of Hausdorff dimension greater than 1. Hence, the hyperbolic dimension of the Julia set is greater than 1.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/16ed10cc2f6af2929a25c318456befea65502d3d

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In Applied Mathematics

1. Walter Bergweiler
2. G. Stallard
3. P. Rippon
4. Lasse Rempe

In Mathematical Physics

1. Walter Bergweiler
2. G. Stallard
3. P. Rippon
4. Lasse Rempe

Citations in the corpus

• Multiply connected wandering domains of entire functions (2011, result): “Much work on the dynamics of entire functions has been concerned with the Speiser class and the Eremenko–Lyubich class, an important tool being a logarithmic change of variable which yields good distortion estimates; see [9, 23, 39, 45, 46] for some results concerning the Eremenko–Lyubich class.”