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arXiv · 2309.09154

Piecewise contracting maps on the interval: Hausdorff dimension, entropy and attractors

A. E. Calderón·E. Villar-Sepúlveda
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Abstract

We consider the attractor $\Lambda$ of a piecewise contracting map $f$ defined on a compact interval. If $f$ is injective, we show that it is possible to estimate the topological entropy of $f$ (according to Bowen's formula) and the Hausdorff dimension of $\Lambda$ via the complexity associated with the orbits of the system. Specifically, we prove that both numbers are zero.

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A. E. Calderón, E. Villar-Sepúlveda. 2023-09-17. Piecewise contracting maps on the interval: Hausdorff dimension, entropy and attractors. https://arxiv.org/abs/2309.09154

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