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Journal Articles Calc. Var. Partial Differential Equations Year : 2017

A multidimensional birkhoff theorem for time-dependent tonelli hamiltonians

Un théorème de Birkhoff multidimensionnel pour les hamiltoniens de Tonelli dépendant du temps

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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Dates and versions

hal-01309652 , version 1 (29-04-2016)
hal-01309652 , version 2 (16-08-2017)

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Marie-Claude Arnaud, Andrea Venturelli. A multidimensional birkhoff theorem for time-dependent tonelli hamiltonians: Birkhoff theorem. Calc. Var. Partial Differential Equations, 2017, 56 (4), pp.122. ⟨hal-01309652v2⟩
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