TL;DR
This paper surveys the concept of type numbers of closed geodesics, discusses Morse theory applications for their existence, and reviews recent advances in variational methods for Finsler and magnetic geodesics.
Contribution
It provides a comprehensive overview of the development and recent progress in the study of closed geodesics using Morse theory and variational techniques.
Findings
Summary of type numbers of closed geodesics
Applications of Morse theory in proving existence
Recent progress in variational methods for Finsler and magnetic 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
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