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Asymptotic escape rates and limiting distributions for multimodal maps
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dc.contributor.author | Demers, Mark | |
dc.contributor.author | Todd, Michael John | |
dc.date.accessioned | 2020-09-08T23:35:55Z | |
dc.date.available | 2020-09-08T23:35:55Z | |
dc.date.issued | 2021-06 | |
dc.identifier | 249327309 | |
dc.identifier | 5b23e0a6-50d6-48d8-a4e3-973c65e77ff1 | |
dc.identifier | 85082538454 | |
dc.identifier | 000645625900004 | |
dc.identifier.citation | Demers , 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.2020.14 | en |
dc.identifier.issn | 0143-3857 | |
dc.identifier.other | ORCID: /0000-0002-0042-0713/work/70619010 | |
dc.identifier.uri | https://hdl.handle.net/10023/20587 | |
dc.description | Funding: MD is partially supported by NSF grant DMS 1800321. | en |
dc.description.abstract | We 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.extent | 50 | |
dc.format.extent | 603714 | |
dc.language.iso | eng | |
dc.relation.ispartof | Ergodic Theory and Dynamical Systems | en |
dc.subject | Multimodal maps | en |
dc.subject | Hofbauer extension | en |
dc.subject | Open systems | en |
dc.subject | Escape rate | en |
dc.subject | Transfer operator | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Asymptotic escape rates and limiting distributions for multimodal maps | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1017/etds.2020.14 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2020-09-09 |
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