Flat metrics are strict local minimizers for the polynomial entropy

Overview & Synopsis

As we have proved in [11], the geodesic flows associated with the flat metrics on T 2 minimize the polynomial entropy h pol. In this paper, we show that, among the geodesic flows that are Bott integrable and dynamically coherent, the geodesic flows associated with flat metrics are local strict minima for h pol. To this aim, we prove a graph property for invariant Lagrangian tori in near-integrable systems.