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On the Kuiper-Kuo Theorem

Published online by Cambridge University Press:  20 November 2018

Chuan I. Chu*
Affiliation:
Department of Mathematics, Hong Kong Baptist College, 224 Waterloo Road, Kowloon, Hong Kong
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Abstract

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In this note we shall give a simple and more direct proof of the Kuiper- Kuo Theorem. Also, we shall simplify Kuiper's proof of the Morse Lemma.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Buchner, M. A., A note on C1 equivalence, J. Math. Anal. Appl. 121 (1987) 9195.Google Scholar
2. Hartman, P., Ordinary Differential Equations, Second Ed. Birkhauser, Boston, 1982.Google Scholar
3. Koike, S., On v-sufficiency and (h̄)-regularity, Publ. Res. Inst. Math. Sci. Kyoto Univ. 17 (1981) 565575.Google Scholar
4. Kuiper, N. H., Cr functions near non-degenerate critical points, Mimeographed, Warwick Univ. 1966.Google Scholar
5. Kuiper, N. H., C1 -equivalence of functions near isolated critical points, Symposium on Infinite Dimensional Topology, No. 69, Princeton Univ. Press, 1972.Google Scholar
6. Kuo, T. C., On C0-sufficiency of jets ofpotential functions, Topology, 8 (1969) 167171.Google Scholar
7. Takens, F., A Note on Sufficiency of Jets, Inventiones Math. 13(1971), 225231.Google Scholar