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Piecewise contractions
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 45 / Issue 5 / May 2025
- Published online by Cambridge University Press:
- 28 October 2024, pp. 1503-1540
- Print publication:
- May 2025
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- Article
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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.
