MERCOLEDI' 23 MAGGIO 2012
14:30-15:30, Sala Conferenze (Puteano, Centro De Giorgi)
SEMINARI DI SISTEMI DINAMICI OLOMORFI
Complexity of geodesic flows on tori"Clémence Labrousse (Institut de Mathématiques de Jussieu (Parigi))
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.