A review of the index method in closed geodesic problem
DOI10.1007/s10114-022-0256-xzbMath1486.53052OpenAlexW4210608442MaRDI QIDQ2075429
Publication date: 14 February 2022
Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10114-022-0256-x
Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Geodesics in global differential geometry (53C22) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Two elliptic closed geodesics on positively curved Finsler spheres
- Two closed geodesics on compact simply connected bumpy Finsler manifolds
- On a conjecture of Anosov
- The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds
- The Fadell-Rabinowitz index and multiplicity of non-contractible closed geodesics on Finsler \(\mathbb{R} P^n\)
- Une théorie de Morse pour les systèmes hamiltoniens convexes
- Closed geodesics on manifolds with infinite Abelian fundamental group
- A new obstruction to embedding Lagrangian tori
- Multiple closed geodesics on bumpy Finsler \(n\)-spheres
- Two closed geodesics on \(\mathbb RP^{2n+1}\) with a bumpy Finsler metric
- Closed geodesics on positively curved Finsler spheres
- Stability of closed geodesics on Finsler 2-spheres
- The index growth and multiplicity of closed geodesics
- Multiple closed geodesics on 3-spheres
- On the average indices of closed geodesics
- Closed geodesics on positively curved manifolds
- Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems
- Geodesics on \(S^ 2\) and periodic points of annulus homeomorphisms
- The homology theory of the closed geodesic problem
- Bott formula of the Maslov-type index theory
- A Maslov-type index theory for symplectic paths
- 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.
- The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form
- Index theory for symplectic paths with applications
- On the average indices of closed geodesics on positively curved Finsler spheres
- Multiple closed geodesics on positively curved Finsler manifolds
- Non-hyperbolic closed geodesics on Finsler spheres
- Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions
- Resonance identity and multiplicity of non-contractible closed geodesics on Finsler \(\mathbb{R} P^n\)
- The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form \(S^{2n+1}/ \Gamma \)
- Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres
- Closed geodesics
- Periodic geodesics on compact Riemannian manifolds
- 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
- The spaces of non-contractible closed curves in compact space forms
- On the iteration of closed geodesics and the sturm intersection theory
- ERGODIC PERTURBATIONS OF DEGENERATE INTEGRABLE HAMILTONIAN SYSTEMS
- Geodesics in Finsler geometry
- Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
- ON THE EXISTENCE OF CLOSED GEODESICS ON TWO-SPHERES
- Existence of closed geodesics on positively curved Finsler manifolds
- The theorem of the three closed geodesics
This page was built for publication: A review of the index method in closed geodesic problem