seminar: The exactness of the Rauzy induction on the space of interval exchange transformations
speaker: Arnaldo Nogueira (Institut de Mathematiques de Marseille)abstract: The homogeneous version of the bi-dimensional Euclidean algorithm is the central motivation for the de nition of multi-dimensional continued fraction algorithms. As examples of such maps, we can mention Jacobi-Perron, Brun, Selmer and Poincaré algorithms. In this class, we also nd the Rauzy induction which acts on the space of interval exchange transformations. In particular, in the case of 2-interval exchanges the Rauzy algorithm coincides with the homogeneous Euclidean algorithm. We recall that, thanks to the work of W. Veech, the Rauzy induction has been a central tool in the study of the dynamical and ergodic properties of interval exchanges. It is known that the Rauzy induction is an ergodic map with respect to Lebesgue measure, although it is dissipative. We will show that this map bares a stronger ergodic property: exactness. So it satis es a 0-1 Kolmogorov law. We will also propose an application of this property to Number Theory.
timetable:
Wed 21 Mar, 14:30 - 15:30, Sala Conferenze Centro De Giorgi
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