Contributions to the study of Anosov geodesic flows in non-compact manifolds

DOI10.3934/dcds.2020223zbMath1467.37038arXiv1810.09998OpenAlexW3033875323MaRDI QIDQ2191143

Sergio Augusto Romaña Ibarra, Ítalo Dowell Lira Melo

Publication date: 24 June 2020

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09998

zbMATH Keywords

Riemannian manifoldconjugate pointsgeodesic flowfocal pointAnosov geodesic flow

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Flows on surfaces (37E35)

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Some rigidity theorems for Anosov geodesic flows in manifolds of finite volume

Cites Work

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• Uniqueness, symmetry, and embeddedness of minimal surfaces
• On the entropy of the geodesic flow in manifolds without conjugate points
• On the creation of conjugate points
• The integral of the scalar curvature of complete manifolds without conjugate points
• Conditions under which a geodesic flow is Anosov
• Geodesic flows
• Ruelle's inequality in negative curvature
• Counterexamples to Ruelle's inequality in the noncompact case
• When is a geodesic flow of Anosov type, I
• Riemannian manifolds with geodesic flow of Anosov type
• A theorem of E. Hopf
• Shorter Notes: Gauss-Bonnet Theorems for Noncompact Surfaces
• On the Variety of Manifolds without Conjugate Points
• Closed Surfaces Without Conjugate Points