Generic hyperbolicity of Aubry sets on surfaces

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

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