|A generalization of the self-dual induction to every interval exchange transformation |
Auteur(s): Ferenczi Sébastien
(Article) Publié: Annales De L'institut Fourier, vol. p. (2014)
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We generalize to all interval exchanges the induction algorithmdefined by Ferenczi and Zamboni for a particular class. Each interval exchangecorresponds to an infinite path in a graph whose vertices are certain unions oftrees we call castle forests. We use it to describe those words obtained by codingtrajectories and give an explicit representation of the system by Rokhlin towers.As an application, we build the first known example of a weakly mixing intervalexchange outside the hyperelliptic and rotations Rauzy classes.