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

A. E. Calderón, E. Villar-Sepúlveda

Published 2023-09-17Version 1

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.