The zero entropy locus for the Lozi maps
Dynamical Systems
2025-08-20 v2
Abstract
We study the zero entropy locus for the Lozi maps. We first define a region in the parameter space and prove that for the parameters in , the Lozi maps have the topological entropy zero. is contained in a larger region where every Lozi map has a unique period-two orbit, and that orbit is attracting. It is easy to see that the zero entropy locus cannot coincide with that larger region since it contains parameters for which the fixed point of the corresponding Lozi map has homoclinic points.
Cite
@article{arxiv.2411.17836,
title = {The zero entropy locus for the Lozi maps},
author = {M. Misiurewicz and S. Štimac},
journal= {arXiv preprint arXiv:2411.17836},
year = {2025}
}