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Pré-Publication, Document De Travail Année : 2017

Cascades in the dynamics of affine interval exchange transformations

Résumé

We describe in this article the dynamics of a 1-parameter family of affine interval exchange transformations. It amounts to studying the directional foliations of a particular affine surface, 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 is done by analysing the dynamics of the Veech group of this surface, combined with an original use of the Rauzy induction in the context of affine interval exchange transformations. Finally, this analysis allows us to completely compute the Veech group of the Disco surface.

Dates et versions

hal-01485286 , version 1 (08-03-2017)

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Adrien Boulanger, Charles Fougeron, Selim Ghazouani. Cascades in the dynamics of affine interval exchange transformations. 2017. ⟨hal-01485286⟩
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