A geometric definition of the Mañé-Mather set and a Theorem of Marie-Claude Arnaud.
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Publication:3108529
DOI10.1017/S0305004111000685zbMath1266.37027MaRDI QIDQ3108529
Patrick Bernard, Joana Oliveira Dos Santos
Publication date: 4 January 2012
Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)
Related Items (9)
Exact Lagrangian submanifolds, Lagrangian spectral invariants and Aubry–Mather theory ⋮ A multidimensional Birkhoff theorem for time-dependent Tonelli Hamiltonians ⋮ When are the invariant submanifolds of symplectic dynamics Lagrangian? ⋮ On the graph theorem for Lagrangian minimizing tori ⋮ Remarks on the symplectic invariance of Aubry-Mather sets ⋮ On the graph theorem for Lagrangian invariant tori with totally irrational invariant sets ⋮ Nonequilibrium thermodynamics as a symplecto-contact reduction and relative information entropy ⋮ Variational and viscosity operators for the evolutionary Hamilton–Jacobi equation ⋮ Tonelli Hamiltonians without conjugate points and \(C^0\) integrability
Cites Work
- On a theorem due to Birkhoff
- Hamiltonian systems, Lagrangian tori and Birkhoff's theorem
- Symplectic topology as the geometry of generating functions
- Hamiltonian diffeomorphisms and Lagrangian distributions
- Lagrangian graphs, minimizing measures and Mañé's critical values
- Variational construction of connecting orbits
- PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians
- Connecting orbits of time dependent Lagrangian systems
- Existence of \(C^1\) critical subsolutions of the Hamilton-Jacobi equation
- Weak KAM theorem on non compact manifolds
- Pseudographs and the Lax–Oleinik semi-group: a geometric and dynamical interpretation
- Lagrangian flows: The dynamics of globally minimizing orbits
- A GEOMETRIC DEFINITION OF THE AUBRY–MATHER SET
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