Orbits closeness for slowly mixing dynamical systems

Abstract

Given a dynamical system, we prove that the shortest distance between two $n$-orbits scales like $n$ to a power even when the system has slow mixing properties, thus building and improving on results of Barros, Liao and the first author. We also extend these results to flows. Finally, we give an example for which the shortest distance between two orbits has no scaling limit.

To appear in Ergodic Theory and Dynamical Systems