Result: Piecewise contractions

Title:
Piecewise contractions
Authors:
JAIN, SAKSHI, LIVERANI, CARLANGELO
Contributors:
Jain, S, Liverani, C
Source:
Ergodic Theory and Dynamical Systems. 45:1503-1540
Publication Status:
Preprint
Publisher Information:
Cambridge University Press (CUP), 2024.
Publication Year:
2024
Subject Terms:
generic properties, FOS: Mathematics, attractors, Dynamical Systems (math.DS), Settore MATH-04/A - Fisica matematica, Mathematics - Dynamical Systems, contracting maps
Document Type:
Academic journal Article
File Description:
application/pdf
Language:
English
ISSN:
1469-4417
0143-3857
DOI:
10.1017/etds.2024.78
DOI:
10.48550/arxiv.2404.02371
Access URL:
http://arxiv.org/abs/2404.02371
Rights:
CC BY
Accession Number:
edsair.doi.dedup.....e17132b69c0fe2ed3e5f78604e2b6e9d
Database:
OpenAIRE

Further Information

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.