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 [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.
Citation
Rousseau , J & Todd , M 2024 , ' Orbits closeness for slowly mixing dynamical systems ' , Ergodic Theory and Dynamical Systems , vol. 44 , no. 4 , pp. 1192 - 1208 . https://doi.org/10.1017/etds.2023.50
Publication
Ergodic Theory and Dynamical Systems
Status
Peer reviewed
ISSN
0143-3857Type
Journal article
Description
Funding: Both 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.Collections
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