Abstract and Applied Analysis
Volume 5 (2000), Issue 2, Pages 113-118
A Morse lemma for degenerate critical points with low differentiability
1Instituto de Matemática, Estatística e Computaçǎo Cientíﬁca (IMECC), Universidade Estadual de Campinas (UNICAMP), CP 6065, CEP, Campinas 13083-970, SP, Brazil
2Instituto de Matemática e Estatística (IME), Universidade Federal de Goiás (UFG), CP 131, CEP, 74001-970, GO, Brazil
Received 30 June 2000
Copyright © 2000 Adriano A. de Moura and Fausto M. de Souza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove a Morse type lemma for, possibly degenerate, critical
points of a function twice strongly differentiable at those points, which allows us to recover, for Finsler metrics, the theorem of Gromoll and Meyer on the existence of infinitely many closed geodesics.