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arXiv · 0704.3087

Hausdorff Dimension of Exponential Parameter Rays and Their Endpoints

Mihai Bailesteanu·Vlad Balan·Dierk Schleicher
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Abstract

We investigate the set $I$ of parameters $κ$ for which the singular value of $z\mapsto e^z+κ$ converges to $\infty$. The set $I$ consists of uncountably many parameter rays, plus landing points of some of these rays. We show that the parameter rays have Hausdorff dimension 1, while the ray endpoints in $I$ alone have dimension 2. Analogous results were known for dynamical planes of exponential maps; our result shows that this also holds in parameter space.

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Mihai Bailesteanu, Vlad Balan, Dierk Schleicher. 2007-11-16. Hausdorff Dimension of Exponential Parameter Rays and Their Endpoints. https://doi.org/10.1088/0951-7715%2F21%2F1%2F006

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