Distributional chaos in shrinking target problems
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.
Authors
- Xueting Tian (ORCID: https://orcid.org/0000-0002-2142-4705)
- Xiaobo Hou (ORCID: https://orcid.org/0000-0002-2437-5814)
- XUTONG ZHAO
Institutions
- Shanghai Jiao Tong University (CN)
- Fudan University (CN)
- Dalian University of Technology (CN)
Publication Details
- Journal
- Ergodic Theory and Dynamical Systems
- Published
- 2026-01-06
- DOI
- https://doi.org/10.1017/etds.2025.10261
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00