Morse index and the stability of closed geodesics

DOI10.1007/s11425-010-0064-0zbMath1209.58012OpenAlexW2130007679MaRDI QIDQ989773

Shanzhong Sun, Xijun Hu

Publication date: 23 August 2010

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-010-0064-0

zbMATH Keywords

stabilityMorse indexclosed geodesic

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Geodesics in global differential geometry (53C22) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items

Minimal \(P\)-symmetric period problem of first-order autonomous Hamiltonian systems ⋮ Instability of closed orbits obtained by minimization* ⋮ Index iteration theories for periodic orbits: old and new ⋮ Conditional Fredholm determinant for the \(S\)-periodic orbits in Hamiltonian systems ⋮ Linear instability for periodic orbits of non-autonomous Lagrangian systems ⋮ Indices and stability of the Lagrangian system on Riemannian manifold ⋮ Minimal period estimates on \(P\)-symmetric periodic solutions of first-order mild superquadratic Hamiltonian systems ⋮ Instability of Periodic Orbits by Conley–Zehnder Index Theory ⋮ Stability of periodic orbits by Conley-Zehnder index theory ⋮ Instability of semi-Riemannian closed geodesics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new obstruction to embedding Lagrangian tori
• Index and stability of symmetric periodic orbits in Hamiltonian systems with application to figure-eight orbit
• Closed geodesics on positively curved manifolds
• Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems
• Iterated index formulae for closed geodesics with applications.
• Index theory for symplectic paths with applications
• 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 Spectral Flow and the Maslov Index
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations