Piecewise contractions
Abstract We study piecewise injective, but not necessarily globally injective, contracting maps on a compact subset of ${\mathbb R}^d$ . 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.
Authors
- Carlangelo Liverani (ORCID: https://orcid.org/0000-0001-8683-4871)
- Sakshi Jain (ORCID: https://orcid.org/0000-0002-4306-0092)
Institutions
- University of Rome Tor Vergata (IT)
- Monash University (AU)
- University of Maryland, College Park (US)
Publication Details
- Journal
- Ergodic Theory and Dynamical Systems
- Published
- 2024-10-28
- DOI
- https://doi.org/10.1017/etds.2024.78
- Citations
- 2
- Primary Topic
- Quantum chaos and dynamical systems
- Type
- article
- Field-Weighted Citation Impact
- 0.56
Funders
- Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers