The type numbers of closed geodesics

Abstract

A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and magnetic geodesics

arXiv comment29 pages, an appendix to the Russian translation of "The calculus of variations in the large" by M. Morse

Cited by in corpus (7)

• Periodic magnetic geodesics on almost every energy level via variational methods
• Two closed orbits for non-degenerate Reeb flows
• The Fadell-Rabinowitz index and multiplicity of non-contractible closed geodesics on Finsler $\mathbb{R}{P}^n$
• Resonance identity and multiplicity of non-contractible closed geodesics on Finsler $\mathbb{R}{P}^n$
• The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form
• The spaces of non-contractible closed curves in compact space forms
• Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions