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dc.contributor.authorDemers, Mark
dc.contributor.authorTodd, Michael John
dc.date.accessioned2020-09-08T23:35:55Z
dc.date.available2020-09-08T23:35:55Z
dc.date.issued2021-06
dc.identifier.citationDemers , M & Todd , M J 2021 , ' Asymptotic escape rates and limiting distributions for multimodal maps ' , Ergodic Theory and Dynamical Systems , vol. 41 , no. 6 , pp. 1656-1705 . https://doi.org/10.1017/etds.2020.14en
dc.identifier.issn0143-3857
dc.identifier.otherPURE: 249327309
dc.identifier.otherPURE UUID: 5b23e0a6-50d6-48d8-a4e3-973c65e77ff1
dc.identifier.otherORCID: /0000-0002-0042-0713/work/70619010
dc.identifier.otherScopus: 85082538454
dc.identifier.otherWOS: 000645625900004
dc.identifier.urihttp://hdl.handle.net/10023/20587
dc.descriptionFunding: MD is partially supported by NSF grant DMS 1800321.en
dc.description.abstractWe consider multimodal maps with holes and study the evolution of the open systems with respect to equilibrium states for both geometric and Hölder potentials. For small holes, we show that a large class of initial distributions share the same escape rate and converge to a unique absolutely continuous conditionally invariant measure; we also prove a variational principle connecting the escape rate to the pressure on the survivor set, with no conditions on the placement of the hole. Finally, introducing a weak condition on the centre of the hole, we prove scaling limits for the escape rate for holes centred at both periodic and non-periodic points, as the diameter of the hole goes to zero.
dc.format.extent50
dc.language.isoeng
dc.relation.ispartofErgodic Theory and Dynamical Systemsen
dc.rightsCopyright © The Author(s) 2020. Published by Cambridge University Press. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/etds.2020.14en
dc.subjectMultimodal mapsen
dc.subjectHofbauer extensionen
dc.subjectOpen systemsen
dc.subjectEscape rateen
dc.subjectTransfer operatoren
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleAsymptotic escape rates and limiting distributions for multimodal mapsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1017/etds.2020.14
dc.description.statusPeer revieweden
dc.date.embargoedUntil2020-09-09


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