Orbits closeness for slowly mixing dynamical systems

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 [On the shortest distance between orbits and the longest common sub...

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Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 44; no. 4; pp. 1192 - 1208
Main Authors ROUSSEAU, JÉRÔME, TODD, MIKE
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.04.2024
Subjects
Original Article
inducing schemes
37A50
longest common substring
shortest distance
correlation dimension
37B20
37D25
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Summary: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 [On the shortest distance between orbits and the longest common substring problem. Adv. Math. 344 (2019), 311–339]. We also extend these results to flows. Finally, we give an example for which the shortest distance between two orbits has no scaling limit.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2023.50