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arXiv · 0902.1065

Dimension properties of the boundaries of exponential basins

Krzysztof Barański·Bogusława Karpińska·Anna Zdunik
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Abstract

We prove that the boundary of a component $U$ of the basin of an attracting periodic cycle (of period greater than 1) for an exponential map on the complex plane has Hausdorff dimension greater than 1 and less than 2. Moreover, the set of points in the boundary of $U$ which do not escape to infinity has Hausdorff dimension (in fact: hyperbolic dimension) greater than 1, while the set of points in the boundary of $U$ which escape to infinity has Hausdorff dimension 1.

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Krzysztof Barański, Bogusława Karpińska, Anna Zdunik. 2009-02-06. Dimension properties of the boundaries of exponential basins. https://doi.org/10.1112/blms%2Fbdp105

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