Polynomial entropy on regular curves
Dynamical Systems
2026-02-24 v1
Abstract
We show that the polynomial entropy of homeomorphisms on regular curves is bounded above by one. Moreover, the polynomial entropy equals one under the fairly mild condition that the homeomorphism possesses a wandering point. We obtain a rigidity result for homeomorphisms on local dendrites (and therefore on graphs and dendrites): their polynomial entropy is either zero or one.
Cite
@article{arxiv.2602.19256,
title = {Polynomial entropy on regular curves},
author = {Maša Đorić and Jelena Katić},
journal= {arXiv preprint arXiv:2602.19256},
year = {2026}
}