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

2023/09/17 by Calderón, A. E., Villar-Sepúlveda, E.
#2022 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.09154

Abstract

We consider the attractor Λ 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 Λ via the complexity associated with the orbits of the system. Specifically, we prove that both numbers are zero.

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