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.
Adriano A. de Moura. Fausto M. de Souza. "A Morse lemma for degenerate critical points with low differentiability." Abstr. Appl. Anal. 5 (2) 113 - 118, 2000. https://doi.org/10.1155/S1085337500000245