Growth rate of periodic orbits for geodesic flows over surfaces with radially symmetric focusing caps

DOI10.3934/jmd.2014.8.139zbMath1351.37152OpenAlexW2322117673MaRDI QIDQ478797

Bryce Weaver

Publication date: 4 December 2014

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jmd.2014.8.139

zbMATH Keywords

periodic orbitsgeodesic flowsnonuniformly hyperbolic systems

Mathematics Subject Classification ID

Periodic orbits of vector fields and flows (37C27) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (2)

Closed geodesics on surfaces without conjugate points ⋮ Symbolic dynamics for three-dimensional flows with positive topological entropy

Cites Work

• An analogue of the prime number theorem for closed orbits of Axiom A flows
• Bernoulli diffeomorphisms on surfaces
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• The uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds
• Generic diffeomorphisms with superexponential growth of number of periodic orbits
• On the mixing property for hyperbolic systems
• Potentials on the two-torus for which the Hamiltonian flow is ergodic
• Geodesic flow on the two-sphere, Part I: Positive measure entropy
• Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems
• Embedded Surfaces with Ergodic Geodesic Flows
• Introduction to Dynamical Systems
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