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A geometric definition of the Mañé-Mather set and a Theorem of Marie-Claude Arnaud.

Published online by Cambridge University Press:  19 October 2011

PATRICK BERNARD  and
JOANA OLIVEIRA DOS SANTOS
PATRICK BERNARD
Affiliation:
Université Paris-Dauphine, ceremade, umr cnrs 7534, Pl. du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16, France e-mail: patrick.bernard@ceremade.dauphine.fr, santos@ceremade.dauphine.fr
JOANA OLIVEIRA DOS SANTOS
Affiliation:
Université Paris-Dauphine, ceremade, umr cnrs 7534, Pl. du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16, France e-mail: patrick.bernard@ceremade.dauphine.fr, santos@ceremade.dauphine.fr
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Abstract

We study some properties of Lipschitz exact Lagrangian manifolds isotopic to the zero section. We prove that if such a manifold is invariant under an optical Hamiltonian, then it must be a Lipschitz graph. This extends a recent result of Marie–Claude Arnaud. We also obtain a new geometric description of the Mañé–Mather invariant set.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 1 , January 2012 , pp. 167 - 178
Copyright
Copyright © Cambridge Philosophical Society 2011

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