Distributional chaos in shrinking target problems
Abstract
Abstract In this article, we prove that the set of well-approximable points $W_\varphi (z) = \{x \in X : d (f^n x, z ) < \varphi (n) \mathrm {\ for\ infinite\ } n \in \mathbb {N}^+\}$ in the shrinking targets problems is distributional chaotic of type 1 for systems with a weak form of the exponential specification property. We apply it to transitive Anosov systems, $\beta $ -shifts, etc.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Mathematical and Theoretical Epidemiology and Ecology Models
Cellular Automata and Applications
Publication details
- Journal / source
- Ergodic Theory and Dynamical Systems
- Volume
- 46
- Issue
- 4
- Pages
- 1020–1042
- Publication date
- 6 January 2026
- Language
- EN