Piecewise Contractions
Dynamical Systems
2025-04-09 v3
Abstract
We study piecewise injective, but not necessarily globally injective, contracting maps on a compact subset of . We prove that generically the attractor and the set of discontinuities of such a map are disjoint, and hence the attractor consists of periodic orbits. In addition, we prove that piecewise injective contractions are generically topologically stable.
Cite
@article{arxiv.2404.02371,
title = {Piecewise Contractions},
author = {Sakshi Jain and Carlangelo Liverani},
journal= {arXiv preprint arXiv:2404.02371},
year = {2025}
}