seminar: Complexity of geodesic flows on tori
speaker: Clémence Labrousse (Institut de Mathématiques de Jussieu, Paris (Analyse Algébrique))abstract: For all the metrics on a surface with genus larger or equal to 2, the geodesic flow has a positive topological entropy, and in this case, the metrics with minimal entropy are known (these are the hyperbolic ones). We are interested in the search of the entropy minimizing metrics for surfaces with genus 1. We first remark that the topological entropy may vanish, this leads us to look at a ''polynomial measure'' of the complexity, namely the polynomial entropy. We will see that the geodesic flows associated with the flat metrics on tori minimize the polynomial entropy. Then, we will show that, among the geodesic flows that are integrable in the Bott sense (with an additional condition of "dynamical coherence") on the 2-torus, the geodesic flows associated with flat metrics are local emph{strict} minima for the polynomial entropy.
timetable:
Wed 23 May, 14:30 - 15:30, Sala Conferenze Centro De Giorgi
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