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arXiv · 0711.2672

Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts

Krzysztof Barański·Bogusława Karpińska·Anna Zdunik
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Abstract

We prove that for meromorphic maps with logarithmic tracts (e.g. entire or meromorphic maps with a finite number of poles from class $\mathcal B$), 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.

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Krzysztof Barański, Bogusława Karpińska, Anna Zdunik. 2007-11-16. Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts. https://doi.org/10.1093/imrn%2Frnn141

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