A MULTIDIMENSIONAL BIRKHOFF THEOREM FOR TIME-DEPENDENT TONELLI HAMILTONIANS: Birkhoff theorem

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.
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https://hal-univ-avignon.archives-ouvertes.fr/hal-01309652
Contributor : Marie-Claude Arnaud <>
Submitted on : Friday, April 29, 2016 - 10:37:10 PM
Last modification on : Tuesday, January 14, 2020 - 10:38:15 AM
Long-term archiving on: Monday, May 23, 2016 - 6:31:48 PM

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  • HAL Id : hal-01309652, version 1
  • ARXIV : 1605.00883

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Marie-Claude Arnaud, Andrea Venturelli. A MULTIDIMENSIONAL BIRKHOFF THEOREM FOR TIME-DEPENDENT TONELLI HAMILTONIANS: Birkhoff theorem. 2016. ⟨hal-01309652v1⟩

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