Gluing-orbit property, local stable/unstable sets, and induced dynamics on hyperspace
Abstract
We prove that local stable/unstable sets of homeomorphisms of an infinite compact metric space satisfying the gluing-orbit property always contain compact and perfect subsets of the space. As a consequence, we prove that if a positively countably expansive homeomorphism satisfies the gluing-orbit property, then the space is a single periodic orbit. We also prove that there are homeomorphisms with gluing-orbit such that its induced homeomorphism on the hyperspace of compact subsets does not have gluing-orbit, contrasting with the case of the shadowing and specification properties, proving that if the induced map has gluing-orbit, then the base map has gluing-orbit and is topologically mixing.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Cellular Automata and Applications
Quantum chaos and dynamical systems
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 558
- Issue
- 1
- Pages
- 130389–130389
- Publication date
- 7 January 2026
- Language
- EN