Les échanges d’intervalles de Veech-Sataev – Sébastien Ferenczi (avec Pascal Hubert)

Sébastien Ferenczi
I2M, CNRS, Marseille
/user/sebastien.ferenczi/

Date(s) : 13/12/2019   iCal
11 h 00 min - 12 h 00 min

We look at d-point extensions of a rotation of angle α with r marked points, generalizing the examples of Veech 1969 and Sataev 1975, together with the square-tiled interval exchanges of [4]. We give conditions for minimality, solving the problem of minimality for Veech 1969, and show that minimality implies unique ergodicity when α has bounded partial quotients. Then we study the property of rigidity, in function of the Ostrowski expansions of the marked points by α: the most interesting case is when α has bounded partial quotients but the natural coding of the rotation with marked points is not linearly recurrent; it is only partially solved but allows us to build the first examples of non linearly recurrent and non rigid interval exchanges. https://hal.archives-ouvertes.fr/hal-02120157/


Veech-Sataev interval exchanges
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