On Finite Quotient Aubry set for Generic Geodesic Flows

Autor: Gonzalo Contreras, José Antônio Gonçalves Miranda
Rok vydání: 2020
Předmět:
Zdroj: Mathematical Physics, Analysis and Geometry. 23
ISSN: 1572-9656
1385-0172
DOI: 10.1007/s11040-020-09336-4
Popis: 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.
Comment: 11 pages, added acknowledgment
Databáze: OpenAIRE
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