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- W2890727280 abstract "We study the structure of the Mather and Aubry sets for the family of lagrangians given by the kinetic energy associated to a riemannian metric $ g$ on a closed manifold $ M$. In this case the Euler-Lagrange flow is the geodesic flow of $(M,g)$. We prove that there exists a residual subset $ mathcal G$ of the set of all conformal metrics to $g$, such that, if $ overline g in mathcal G$ then the corresponding geodesic flow has a finitely many ergodic c-minimizing measures, for each non-trivial cohomology class $ c in H^1(M,mathbb{R})$. This implies that, for any $ c in H^1(M,mathbb{R})$, the quotient Aubry set for the cohomology class c has a finite number of elements for this particular family of lagrangian systems." @default.
- W2890727280 created "2018-09-27" @default.
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- W2890727280 date "2020-04-28" @default.
- W2890727280 modified "2023-10-15" @default.
- W2890727280 title "On Finite Quotient Aubry set for Generic Geodesic Flows" @default.
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- W2890727280 doi "https://doi.org/10.1007/s11040-020-09336-4" @default.
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