Orbits closeness for slowly mixing dynamical systems
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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.
Rousseau , J & Todd , M 2023 , ' Orbits closeness for slowly mixing dynamical systems ' , Ergodic Theory and Dynamical Systems , vol. FirstView . https://doi.org/10.1017/etds.2023.50
Ergodic Theory and Dynamical Systems
Copyright © The Author(s), 2023. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
DescriptionBoth authors were partially supported by FCT projects PTDC/MAT-PUR/28177/2017 and by CMUP (UIDB/00144/2020), which is funded by FCT with national (MCTES) and European structural funds through the programs FEDER, under the partnership agreement PT2020. JR was also partially supported by CNPq and PTDC/MATPUR/4048/2021, and with national funds.
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