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

A. E. Calderón; E. Villar-Sepúlveda

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

Dynamical Systems 2023-09-19 v1

Authors: A. E. Calderón , E. Villar-Sepúlveda

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.

Keywords

hausdorff measure and dimension attractors topological entropy

Cite

@article{arxiv.2309.09154,
  title  = {Piecewise contracting maps on the interval: Hausdorff dimension, entropy and attractors},
  author = {A. E. Calderón and E. Villar-Sepúlveda},
  journal= {arXiv preprint arXiv:2309.09154},
  year   = {2023}
}

Comments

8 pages

Related papers

View all related →