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arXiv · 2404.02371

Piecewise Contractions

Sakshi Jain·Carlangelo Liverani
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Abstract

We study piecewise injective, but not necessarily globally injective, contracting maps on a compact subset of \(\bR^d\). 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.

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Sakshi Jain, Carlangelo Liverani. 2024-04-03. Piecewise Contractions. https://doi.org/10.1017/etds.2024.78

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