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Orbits closeness for slowly mixing dynamical systems

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dc.contributor.authorRousseau, Jerome
dc.contributor.authorTodd, Mike
dc.date.accessioned2023-07-24T16:30:03Z
dc.date.available2023-07-24T16:30:03Z
dc.date.issued2024-04
dc.identifier266825094
dc.identifier6a53cccc-6cf1-4025-b823-b0ad1a467f92
dc.identifier85166568041
dc.identifier.citationRousseau , 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.2023.50en
dc.identifier.issn0143-3857
dc.identifier.otherORCID: /0000-0002-0042-0713/work/139553708
dc.identifier.urihttps://hdl.handle.net/10023/28017
dc.descriptionFunding: 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.en
dc.description.abstractGiven 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.
dc.format.extent17
dc.format.extent272805
dc.language.isoeng
dc.relation.ispartofErgodic Theory and Dynamical Systemsen
dc.subjectShortest distanceen
dc.subjectLongest common substringen
dc.subjectCorrelation dimensionen
dc.subjectInducing schemesen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleOrbits closeness for slowly mixing dynamical systemsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.identifier.doihttps://doi.org/10.1017/etds.2023.50
dc.description.statusPeer revieweden


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