Generic hyperbolicity of Aubry sets on surfaces

Gonzalo Contreras (1) , Alessio Figalli (2) , Ludovic Rifford (3, 4)

1 CIMAT - Centro de Investigación en Matemáticas
2 Department of Mathematics and Statistics [Texas Tech]
3 McTAO - Mathematics for Control, Transport and Applications
4 LJAD - Laboratoire Jean Alexandre Dieudonné

Given a Tonelli Hamiltonian of class C2 on the cotangent bundle of a compact surface, we show that there is an open dense set of potentials in the C2 topology for which the Aubry set is hyperbolic in its energy level.

Domaines: Systèmes dynamiques [math.DS]

Gonzalo Contreras, Alessio Figalli, Ludovic Rifford. Generic hyperbolicity of Aubry sets on surfaces. Inventiones Mathematicae, 2015, 200 (1). ⟨hal-00935976⟩