97-470 G. Contreras, J. Delgado, R. Iturriaga

Lagrangian Flows: The Dynamics of Globally Minimizing Orbits - II (100K, LaTeX) Sep 2, 97

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Abstract. Define the critical level c(L) of a convex superlinear autonomous Lagrangian L as the infimum of the k's such that the Lagrangian L+k has minimizers with fixed endpoints and free time interval. We provide proofs for Mañé's statements characterizing c(L) in terms of minimizing measures for L, and also giving graph, recurrence, covering and cohomology properties for minimizers of L+c(L). It is also proven that the minimizers of L+c(L) are in the energy level E=c(L) and that c(L) is the infimum of the energy levels k such that the following form of Tonelli's theorem holds: there exist minimizers of the (L+k)-action joining any two points in the projection of E=k among curves with energy k.

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