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arXiv · 1203.2724

Topological pressure and fractal dimensions of cookie-cutter-like sets

Mrinal Kanti Roychowdhury
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Abstract

The cookie-cutter-like set is defined as the limit set of a sequence of classical cookie-cutter mappings. For this cookie-cutter set it is shown that the topological pressure function exists, and that the fractal dimensions such as the Hausdorff dimension, the packing dimension and the box-counting dimension are all equal to the unique zero $h$ of the pressure function. Moreover, it is shown that the $h$-dimensional Hausdorff measure and the $h$-dimensional packing measure are finite and positive.

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Mrinal Kanti Roychowdhury. 2012-03-13. Topological pressure and fractal dimensions of cookie-cutter-like sets. https://arxiv.org/abs/1203.2724

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