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The tiered Aubry set for autonomous Lagrangian functions

Marie-Claude Arnaud — 2008

Annales de l’institut Fourier

Let L : T M → ℝ be a Tonelli Lagrangian function (with M compact and connected and dim M ≥ 2 ). The tiered Aubry set (resp. Mañé set) 𝒜 T ( L ) (resp. 𝒩 T ( L ) ) is the union of the Aubry sets (resp. Mañé sets) 𝒜 ( L + λ ) (resp. 𝒩 ( L + λ ) ) for λ closed 1-form. Then the set 𝒩 T ( L ) is closed, connected and if dim H 1 ( M ) ≥ 2 , its intersection with any energy level is connected and chain transitive; ...

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