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  Cascades in the dynamics of affine interval exchange transformations

Boulanger, A., Fougeron, C., & Ghazouani, S. (2020). Cascades in the dynamics of affine interval exchange transformations. Ergodic Theory and Dynamical Systems, 40(8), 2073-2097. doi:10.1017/etds.2018.141.

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Boulanger, Adrien, Author
Fougeron, Charles1, Author           
Ghazouani, Selim, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Dynamical Systems
 Abstract: We describe in this article the dynamics of a one-parameter family of affine interval exchange transformations. This amounts to studying the directional foliations of a particular dilatation surface introduced in Duryev et al [Affine surfaces and their Veech groups. Preprint, 2016, arXiv:1609.02130], the Disco surface. We show that this family displays various dynamical behaviours: it is generically dynamically trivial but for a Cantor set of parameters the leaves of the foliations accumulate to a (transversely) Cantor set. This study is achieved through analysis of the dynamics of the Veech group of this surface combined with a modified version of Rauzy induction in the context of affine interval exchange transformations.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 25
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 Table of Contents: -
 Rev. Type: Peer
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Title: Ergodic Theory and Dynamical Systems
Source Genre: Journal
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Publ. Info: Cambridge University Press
Pages: - Volume / Issue: 40 (8) Sequence Number: - Start / End Page: 2073 - 2097 Identifier: -