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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
##### Keywords:
Lagrangian flows; ergodic theory; closed manifolds
Full Text:
##### References:
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