Inventiones mathematicae

, Volume 200, Issue 1, pp 201–261 | Cite as

Generic hyperbolicity of Aubry sets on surfaces

  • G. Contreras
  • A. FigalliEmail author
  • L. Rifford


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.



Large part of this work was done while AF and GC were visiting the Mathematics Department at the University Nice Sophia Antipolis, whose warm hospitality is gratefully acknowledged. The authors would like to thank the anonymous referees for their valuable comments and suggestions to improve the quality of the paper.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.CIMATGuanajuato GTOMexico
  2. 2.Department of MathematicsThe University of Texas at AustinAustinUSA
  3. 3.Université Nice Sophia Antipolis, Laboratoire J.A. Dieudonné, UMR 7351Nice Cedex 2France

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