 97470 G. Contreras, J. Delgado, R. Iturriaga
 Lagrangian Flows: The Dynamics of Globally Minimizing Orbits  II
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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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