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The Morse Lemma in Infinite Dimensions via Singularity Theory

Golubitsky, Martin and Marsden, Jerrold (1983) The Morse Lemma in Infinite Dimensions via Singularity Theory. SIAM Journal on Mathematical Analysis, 14 (6). pp. 1037-1044. ISSN 0036-1410. http://resolver.caltech.edu/CaltechAUTHORS:GOLsiamjma83

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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 in discussed.


Item Type:Article
Additional Information:©1983 Society for Industrial and Applied Mathematics Received by the editors June 28, 1982, and in revised form October 29, 1982.
Record Number:CaltechAUTHORS:GOLsiamjma83
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:GOLsiamjma83
Alternative URL:http://dx.doi.org/10.1137/0514083
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4638
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:30 Aug 2006
Last Modified:26 Dec 2012 09:00

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