Abstract : Let M be a closed and connected manifold, H : T * M × R/Z → R a Tonelli 1-periodic Hamiltonian and L ⊂ T * M a Lagrangian submanifold Hamiltonianly isotopic to the zero section. We prove that if L is invariant by the time-one map of H, then L is a graph over M. An interesting consequence in the autonomous case is that in this case, L is invariant by all the time t maps of the Hamiltonian flow of H.
https://hal-univ-avignon.archives-ouvertes.fr/hal-01309652
Contributor : Marie-Claude Arnaud
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Submitted on : Wednesday, August 16, 2017 - 5:19:55 PM
Last modification on : Tuesday, January 14, 2020 - 10:38:15 AM
