# A constructive induction for interval exchanges and applications

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Sébastien Ferenczi , Institut de Mathématiques de Marseille
Fine Hall 601

We explain the induction process initiated by L. Zamboni and myself, which was designed to understand the word combinatorics of the natural codings, but is now better described through a geometrical model introduced by Delecroix and Ulcigrai, with a natural extension where convex polygons (parallelograms in the hyperelliptic case) replace the rectangles of the Rauzy-Veech induction. This induction is used to build families of examples of interval exchange transformations, with weak mixing or with eigenvalues, with Veech's simplicity property, or satisfying a criterion due to Bourgain which in turn implies Sarnak's conjecture on the orthogonality of the trajectories with the Moebius function.