The type numbers of closed geodesics. (English) Zbl 1229.58015
Summary: This is 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.
MSC:
| 58E10 | Variational problems in applications to the theory of geodesics (problems in one independent variable) |
| 53C22 | Geodesics in global differential geometry |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
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