Shortest distance between partial orbits
Abstract
Inspired by the work of Barros, Liao, and Rousseau (Adv. Math. 334 (2019) 311-339), in this paper we ask whether an analogous result holds for partial orbits. Letting $ \{a_{k}\}\subset \mathbb{N}, $ we study the shortest distance between the $ a_{k} $ iterates of two points in a dynamical system. We prove that under some mixing conditions, the asymptotic behavior of the shortest distance between the $ a_{k} $ iterates converges and the limit depends on the correlation dimension and the logarithmic density of $ \{a_{k}\}. $
Fields of Study & Subjects
Mathematical Dynamics and Fractals
advanced mathematical theories
Advanced Topology and Set Theory
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Volume
- 30
- Issue
- 0
- Pages
- 487–494
- Publication date
- 1 January 2026
- Language
- EN