This book contains expository lectures from the CBMS Regional Conference held at the University of Florida, 1982.

The author considers a space formed by all closed curves in which the closed geodesics are characterized as the critical points of a functional, an idea going back to Morse. This exposition gives a refined version of Morse's approach which has several advantages over the old one--in particular, it possesses a canonical $\mathbf O(2)$-action.

Readership

Table of Contents

• The Hilbert manifold of $H^1$-curves
• The loop space and the space of closed curves
• The second order neighborhood of a critical point Appendix. The $S^1$- and the $Z_2$-action on $\Lambda M$
• Closed geodesics on spheres
• On the existence of infinitely many closed geodesics