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Lagrangian flows: the dynamics of globally minimizing orbits. II. (English) Zbl 0892.58065

Let the critical level \(c(L)\) of a convex superlinear Lagrangian \(L\) be the infimum of reals \(k\) such that the Lagrangian \(L+k\) has minimizers with fixed endpoints and free time interval.
The authors provide the proofs of theorems characterizing \(c(L)\) in terms of minimizing measures of \(L\). There are proved results for cohomology properties for minimizers of \(L+c(L)\). The following Tonelli’s theorem is proved: There exist minimizers of the \(L+k\)-action joining any two points in the projection of \(E=k\) among curves with energy \(k\). [For Part I, see R. Mañé, ibid., 141-153 (1997; Zbl 0892.58064) see the review above].
Reviewer: S.Nenov (Sofia)

MSC:

37C10 Dynamics induced by flows and semiflows
37A99 Ergodic theory

Citations:

Zbl 0892.58064
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References:

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