Orbits closeness for slowly mixing dynamical systems

2022/09/14 by Jérôme Rousseau, Rousseau, Jerome, Mike Todd +1 · 2 citations
Mathematics · #37A50 #37B20 #37D25 #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2209.06594

openalex publication_date 2022/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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