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Lagrangian flows: The dynamics of globally minimizing orbits-II

Lagrangian flows: The dynamics of globally minimizing orbits-II Define the critical levelc(L) of a convex superlinear LagragianL as the infimum of thek ∈ ℝsuch that the LagragianL+k has minimizers with fixed endpoints and free time interval. We provide proofs for Mañé's statements [7] characterizingc(L) in termos of minimizing measures ofL, and also giving graph, recurrence covering and cohomology properties for minimizers ofL+c(L). It is also proven thatc(L) is the infimum of the energy levelsk such that the following for of Tonelli's theorem holds:There exists minimizers of the L+k-action joining any two points in the projection of E=k among curves with energy k. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Lagrangian flows: The dynamics of globally minimizing orbits-II

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References (7)

Publisher
Springer Journals
Copyright
Copyright © 1997 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/BF01233390
Publisher site
See Article on Publisher Site

Abstract

Define the critical levelc(L) of a convex superlinear LagragianL as the infimum of thek ∈ ℝsuch that the LagragianL+k has minimizers with fixed endpoints and free time interval. We provide proofs for Mañé's statements [7] characterizingc(L) in termos of minimizing measures ofL, and also giving graph, recurrence covering and cohomology properties for minimizers ofL+c(L). It is also proven thatc(L) is the infimum of the energy levelsk such that the following for of Tonelli's theorem holds:There exists minimizers of the L+k-action joining any two points in the projection of E=k among curves with energy k.

Journal

Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals

Published: Feb 11, 2005

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