Two Remarks about Mañé’s Conjecture
نویسنده
چکیده
In this note we consider an autonomous Tonelli Lagrangian L on a closed manifold M , that is, a C2 function L : TM −→ R such that L is fiberwise strictly convex and superlinear. Then the Euler-Lagrange equation associated with L defines a complete flow φt on TM . Define Minv to be the set of Φt-invariant, compactly supported, Borel probability measures on TM . Mather showed that the function (called action of the Lagrangian on measures) Minv −→ R μ 7−→ ∫
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