Calculus of Variations and Geometric Measure Theory

G. Contreras - A. Figalli - L. Rifford

Generic hyperbolicity of Aubry sets on surfaces

created by figalli on 07 Jul 2014


Accepted Paper

Inserted: 7 jul 2014
Last Updated: 7 jul 2014

Journal: Invent. Math.
Year: 2014


Given a Tonelli Hamiltonian of class $C^2$ on the cotangent bundle of a compact surface, we show that there is an open dense set of potentials in the $C^2$ topology for which the Aubry set is hyperbolic in its energy level.