Piecewise continuous and monotonic maps on the interval
Dynamical Systems
2026-04-07 v3
Abstract
Let be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous case. We define and study the notion of closed structure, which can be seen as an generalization of periodic orbit. We also study the periodic orbits that are away from the discontinuities of , extending the notion of trapped and free orbits.
Cite
@article{arxiv.2405.04452,
title = {Piecewise continuous and monotonic maps on the interval},
author = {Kleyber Cunha and Marcio Gouveia and Paulo Santana},
journal= {arXiv preprint arXiv:2405.04452},
year = {2026}
}
Comments
There are flaws in the notion of transportation of intervals of Definition 2. We are grateful to the anonymous reviewers for pointing them. This manuscript should not be used or cited