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The horse-shoe and spinning diffeomorphisms

Published online by Cambridge University Press:  24 October 2008

D. K. Arrowsmith
D. K. Arrowsmith
Affiliation:
University of Southampton
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Extract

In (5), a generalization of a Morse-Smale diffeomorphism known as a Smale diffeomorphism is given and all such diffeomorphisms are shown to be C° dense on a C∞ compact manifold and structurally stable. Also Morse inequalities for Smale diffeomorphisms are given which supersede the classical Morse-Smale inequalities (3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 53 - 55
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Armstrong, M. A.Compact Čech Cohomology (Lecture Notes by E. C. Zeeman, University of Warwick, 1965).Google Scholar
(2)Arrowsmith, D. K. Ph.D. Thesis, Leicester University (unpublished).Google Scholar
(3)Smale, S.Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967).Google Scholar
(4)Williams, R. F.Non-compact Lie group actions. Proc. Con. Transformation Groups, New Orleans, 1967.Google Scholar
(5)Zeeman, E. C. Morse Inequalities for Smale Diffeomorphisms and Flows (to appear).Google Scholar