Abstract and Applied Analysis
Volume 5 (2000), Issue 2, Pages 113-118
doi:10.1155/S1085337500000245
A Morse lemma for degenerate critical points with low differentiability
Adriano A. De Moura1
and Fausto M. De Souza2
1Instituto de Matemática, Estatística e Computaç {a}o 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
Abstract
We prove a Morse type lemma for, possibly degenerate, critical points of a C1 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.