On a conjecture of Anosov

DOI10.1016/j.aim.2012.04.006zbMath1261.53038arXiv1112.5234OpenAlexW2963840860WikidataQ123114879 ScholiaQ123114879MaRDI QIDQ436119

Wei Wang

Publication date: 30 July 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.5234

zbMATH Keywords

stabilityclosed geodesicsFinsler spheresbumpy Finsler metricindex iterationmean index identity

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items (20)

Two elliptic closed geodesics on positively curved Finsler spheres ⋮ Homogeneous Finsler spaces with only one orbit of prime closed geodesics ⋮ The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form ⋮ Resonance identity and multiplicity of non-contractible closed geodesics on Finsler \(\mathbb{R} P^n\) ⋮ Lusternik-Schnirelmann theory and closed Reeb orbits ⋮ The irrational ratio of average indices of closed geodesics on positively curved Finsler spheres ⋮ The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form \(S^{2n+1}/ \Gamma \) ⋮ Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics ⋮ Index iteration theories for periodic orbits: old and new ⋮ On the minimal number of periodic orbits on some hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds ⋮ Multiplicity of periodic orbits for dynamically convex contact forms ⋮ Multiple closed geodesics on positively curved Finsler manifolds ⋮ Closed Geodesics on Positively Curved Finsler 3-Spheres ⋮ The Fadell-Rabinowitz index and multiplicity of non-contractible closed geodesics on Finsler \(\mathbb{R} P^n\) ⋮ Finsler spheres with constant flag curvature and finite orbits of prime closed geodesics ⋮ The non-contractibility of closed geodesics on Finsler \(\mathbb{R} P^n\) ⋮ A review of the index method in closed geodesic problem ⋮ A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem ⋮ Multiplicity of non-contractible closed geodesics on Finsler compact space forms

Cites Work

• Multiple closed geodesics on bumpy Finsler \(n\)-spheres
• Closed geodesics on positively curved Finsler spheres
• The length of a shortest geodesic loop
• Stability of closed geodesics on Finsler 2-spheres
• The index growth and multiplicity of closed geodesics
• Multiple closed geodesics on 3-spheres
• Existence of closed geodesics on positively curved manifolds
• On the average indices of closed geodesics
• Closed geodesics on positively curved manifolds
• Bott formula of the Maslov-type index theory
• A sphere theorem for non-reversible Finsler metrics
• Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics
• Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)
• Iterated index formulae for closed geodesics with applications.
• Index theory for symplectic paths with applications
• Equivariant Morse theory and closed geodesics
• The relation of the Morse index of closed geodesics with the Maslov-type index of symplectic paths
• The existence of two closed geodesics on every Finsler 2-sphere
• On the iteration of closed geodesics and the sturm intersection theory
• The second closed geodesic on Finsler spheres of dimension 𝑛>2
• ERGODIC PERTURBATIONS OF DEGENERATE INTEGRABLE HAMILTONIAN SYSTEMS
• Geodesics in Finsler geometry
• Geometry of the Katok examples
• Existence of closed geodesics on positively curved Finsler manifolds
• Riemannian geometry
• Index parity of closed geodesics and rigidity of Hopf fibrations
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