1997
DOI: 10.1007/bf01233390
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Lagrangian flows: The dynamics of globally minimizing orbits-II

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Cited by 74 publications
(99 citation statements)
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“…The problem we consider here is in some sense analogous (although we do not consider the homological position) to the problems considered in Aubry-Mather theory (see [6,18]) for Lagrangian flows. A recent result of Mañé (see [18] and also [5,6]) on Lagrangian flows shows that generically on the Lagrangian there is a unique measure minimizing…”
Section: A Measure In M(f ) Is Called a Lyapunov Minimizing Measurementioning
confidence: 99%
See 1 more Smart Citation
“…The problem we consider here is in some sense analogous (although we do not consider the homological position) to the problems considered in Aubry-Mather theory (see [6,18]) for Lagrangian flows. A recent result of Mañé (see [18] and also [5,6]) on Lagrangian flows shows that generically on the Lagrangian there is a unique measure minimizing…”
Section: A Measure In M(f ) Is Called a Lyapunov Minimizing Measurementioning
confidence: 99%
“…A recent result of Mañé (see [18] and also [5,6]) on Lagrangian flows shows that generically on the Lagrangian there is a unique measure minimizing…”
Section: A Measure In M(f ) Is Called a Lyapunov Minimizing Measurementioning
confidence: 99%
“…Let π : T M → M the canonical projection. Then π| b Σ : Σ → M is a bijective map with Lipschitz inverse, the proof of this property can be seen in [8,theorem VI] and is a extension of the Mather's graph theorem [25, theorem 2].…”
Section: 3mentioning
confidence: 99%
“…We recall the definition of the strict Mañé's critical value for convex and superlinear lagrangians (cf. [23,8] It is well known that for an arbitrary surface M , if Ω = dη and c > c 0 (L η ), then the restriction of the exact magnetic flow in the energy set T c M is a reparametrization of a geodesic flow in the unit tangent bundle for an appropriate Finsler metric on M (cf. [9]).…”
Section: Introduction and Statementsmentioning
confidence: 99%
“…In fact, it follows ( [22], [10]) that D E (x, y) = −∞ for E < E and D E (x, x) = 0 for E ≥ E and any x, y ∈ M .…”
Section: Introductionmentioning
confidence: 99%