Files in this item
Recurrence statistics for the space of interval exchange maps and the Teichmüller flow on the space of translation surfaces
Item metadata
dc.contributor.author | Aimino, Romain | |
dc.contributor.author | Nicol, Matthew | |
dc.contributor.author | Todd, Michael John | |
dc.date.accessioned | 2017-08-08T08:30:11Z | |
dc.date.available | 2017-08-08T08:30:11Z | |
dc.date.issued | 2017-08 | |
dc.identifier.citation | Aimino , R , Nicol , M & Todd , M J 2017 , ' Recurrence statistics for the space of interval exchange maps and the Teichmüller flow on the space of translation surfaces ' , Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques , vol. 53 , no. 3 , pp. 1371-1401 . https://doi.org/10.1214/16-AIHP758 | en |
dc.identifier.issn | 0246-0203 | |
dc.identifier.other | PURE: 52377395 | |
dc.identifier.other | PURE UUID: 958d777d-f5e7-4494-bfe7-2fba0c918566 | |
dc.identifier.other | Scopus: 85025437705 | |
dc.identifier.other | ORCID: /0000-0002-0042-0713/work/54181516 | |
dc.identifier.other | WOS: 000406982900013 | |
dc.identifier.uri | https://hdl.handle.net/10023/11400 | |
dc.description | MT was partially supported by NSF grant DMS 110958. | en |
dc.description.abstract | In this paper we show that the transfer operator of a Rauzy–Veech–Zorich renormalization map acting on a space of quasi-Hölder functions is quasicompact and derive certain statistical recurrence properties for this map and its associated Teichmüller flow. We establish Borel–Cantelli lemmas, Extreme Value statistics and return time statistics for the map and flow. Previous results have established quasicompactness in Hölder or analytic function spaces, for example the work of M. Pollicott and T. Morita. The quasi-Hölder function space is particularly useful for investigating return time statistics. In particular we establish the shrinking target property for nested balls in the setting of Teichmüller flow. Our point of view, approach and terminology derive from the work of M. Pollicott augmented by that of M. Viana. | |
dc.language.iso | eng | |
dc.relation.ispartof | Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques | en |
dc.rights | © 2017, Association des Publications de l’Institut Henri Poincaré. This work has been made available online in accordance with the publisher’s policies. This is the final published version of the work, which was originally published at projecteuclid.org / https://doi.org/10.1214/16-AIHP758 | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Recurrence statistics for the space of interval exchange maps and the Teichmüller flow on the space of translation surfaces | en |
dc.type | Journal article | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1214/16-AIHP758 | |
dc.description.status | Peer reviewed | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.