A GEOMETRIC DEFINITION OF THE AUBRY–MATHER SET

DOI10.1142/S1793525310000343zbMath1200.37055MaRDI QIDQ4930571

Patrick Bernard, Joana Oliveira Dos Santos

Publication date: 29 September 2010

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

zbMATH Keywords

symplectic geometryLagrangian systemsAubry setweak KAM theory

Mathematics Subject Classification ID

Symplectic and contact topology in high or arbitrary dimension (57R17) Lagrangian submanifolds; Maslov index (53D12)

Related Items (3)

Exact Lagrangian submanifolds, Lagrangian spectral invariants and Aubry–Mather theory ⋮ Remarks on the symplectic invariance of Aubry-Mather sets ⋮ A geometric definition of the Mañé-Mather set and a Theorem of Marie-Claude Arnaud.

Cites Work

• Symplectic topology as the geometry of generating functions
• 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
• Lagrangian flows: The dynamics of globally minimizing orbits
• State Constraints in Convex Control Problems of Bolza

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