English

Flat metrics are local strict minimizers for the polynomial entropy

Dynamical Systems 2012-07-23 v1 Differential Geometry

Abstract

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

Keywords

Cite

@article{arxiv.1207.4934,
  title  = {Flat metrics are local strict minimizers for the polynomial entropy},
  author = {Clémence Labrousse},
  journal= {arXiv preprint arXiv:1207.4934},
  year   = {2012}
}

Comments

15 pages

R2 v1 2026-06-21T21:39:01.971Z