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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, SP 13083-970, Brazil
2Instituto de Matemática e Estatística (IME), Universidade Federal de Goiás (UFG), CP 131, CEP, GO 74001-970, Brazil

Received 30 June 2000

Copyright © 2000 Hindawi Publishing Corporation. 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 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.