Multiplicity and stability of closed geodesics on Finsler 2-spheres

DOI10.4171/JEMS/56zbMath1099.53036OpenAlexW3146898531MaRDI QIDQ2502558

Long, Yiming

Publication date: 13 September 2006

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/56

zbMATH Keywords

closed geodesicsFinsler manifoldsFinsler 2-spheres

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) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (27)

Two elliptic closed geodesics on positively curved Finsler spheres ⋮ Multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics ⋮ Multiple closed geodesics on Riemannian 3-spheres ⋮ Multiple closed geodesics on bumpy Finsler \(n\)-spheres ⋮ 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 \(\mathbb{R} P^n\) ⋮ Some topics in differential geometry of normed spaces ⋮ Two closed geodesics on \(\mathbb RP^{2n+1}\) with a bumpy Finsler metric ⋮ 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 ⋮ The type numbers of closed geodesics ⋮ The length of a shortest geodesic loop ⋮ The second closed geodesic on Finsler spheres of dimension 𝑛>2 ⋮ Stability of closed geodesics on Finsler 2-spheres ⋮ The second closed geodesic on a complex projective plane ⋮ Collection of problems proposed at International Conference on Variational Methods ⋮ The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds ⋮ Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres ⋮ Index iteration theory for symplectic paths and multiple periodic solution orbits ⋮ Closed Geodesics on Positively Curved Finsler 3-Spheres ⋮ The index growth and multiplicity of closed geodesics ⋮ Multiple closed geodesics on 3-spheres ⋮ On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths ⋮ The non-contractibility of closed geodesics on Finsler \(\mathbb{R} P^n\) ⋮ Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions ⋮ Open problems and questions about geodesics

Cites Work

• Unnamed Item
• Existence of closed geodesics on positively curved manifolds
• Geodätische Linien auf Riemannschen Mannigfaltigkeiten
• Closed geodesics on positively curved manifolds
• Geodesics in Finsler geometry
• ON THE EXISTENCE OF CLOSED GEODESICS ON TWO-SPHERES

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