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Cascades in the dynamics of affine interval exchange transformations
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Boulanger, Adrien, Fougeron, Charles and Ghazouani, Selim (2020) Cascades in the dynamics of affine interval exchange transformations. Ergodic Theory and Dynamical Systems, 40 (8). pp. 2073-2097. doi:10.1017/etds.2018.141 ISSN 0143-3857.
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Official URL: http://dx.doi.org/10.1017/etds.2018.141
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.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||||
| Publisher: | Cambridge University Press | ||||||
| ISSN: | 0143-3857 | ||||||
| Official Date: | August 2020 | ||||||
| Dates: |
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| Volume: | 40 | ||||||
| Number: | 8 | ||||||
| Page Range: | pp. 2073-2097 | ||||||
| DOI: | 10.1017/etds.2018.141 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access |
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