We study piecewise injective, but not necessarily globally injective, contracting maps on a compact subset of Rd. 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.
Jain, S., Liverani, C. (2024). Piecewise contractions. ERGODIC THEORY & DYNAMICAL SYSTEMS, 1-38 [10.1017/etds.2024.78].
Piecewise contractions
JAIN, SAKSHI
;LIVERANI, CARLANGELO
2024-01-01
Abstract
We study piecewise injective, but not necessarily globally injective, contracting maps on a compact subset of Rd. 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.File in questo prodotto:
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