M. Golubitsky and J. Marsden

The Morse lemma in infinite dimensions via singularity theory

SIAM J. Math. Anal. 14 (1983) 1037-1044.

• Abstract

An infinite dimensional Morse lemma is proved using the deformation lemma from singularity theory. It is shown that the versions of the Morse lemmas due to Palais and Tromba are special cases. An infinite dimensional splitting lemma is proved. The relationship of the work here to other approaches in the literature is discussed.