Recurrence statistics for the space of interval exchange maps and the Teichmüller flow on the space of translation surfaces

Romain Aimino, Matthew Nicol, Michael John Todd

Research output: Contribution to journalArticlepeer-review

2 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)1371-1401
JournalAnnales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Volume53
Issue number3
Early online date21 Jul 2017
DOIs
Publication statusPublished - Aug 2017

Fingerprint

Dive into the research topics of 'Recurrence statistics for the space of interval exchange maps and the Teichmüller flow on the space of translation surfaces'. Together they form a unique fingerprint.

Cite this