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A note on expansiveness and hyperbolicity for generic geodesic flows
Autores
Orientador(es)
Resumo(s)
In this short note we contribute to the generic dynamics of geodesic flows associated to metrics on compact Riemannian manifolds of dimension ≥ 2. We prove that there exists a C2-residual subset R of metrics on a given compact Riemannian manifold such that if g∈R, then its associated geodesic flow φ_g(t) is expansive if and only if the closure of the set of periodic orbits of φgt is a uniformly hyperbolic set.
For surfaces, we obtain a stronger statement: there exists a C2-residual R such that if g ∈ R, then its associated geodesic flow φgt is expansive if and only if φ_g(t) is an Anosov flow.
Descrição
Palavras-chave
Expansiveness Residual sets Anosov Geodesic flows
Contexto Educativo
Citação
M. Bessa, A Note on Expansiveness and Hyperbolicity for Generic Geodesic Flows, Mathematical Physics, Analysis and Geometry, 21, 2, 2018
Editora
Springer