Cascades in the dynamics of affine interval exchange transformations
Dynamical Systems
2020-07-15 v4
Abstract
We describe in this article the dynamics of a -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. s study is achieved through the analysis the dynamics of the Veech group of this surface combined a modified version of Rauzy induction in the context of affine interval exchange transformations.
Keywords
Cite
@article{arxiv.1701.02332,
title = {Cascades in the dynamics of affine interval exchange transformations},
author = {Adrien Boulanger and Charles Fougeron and Selim Ghazouani},
journal= {arXiv preprint arXiv:1701.02332},
year = {2020}
}