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Combined structural and topological stability are equivalent to Axiom A and the strong transversality condition

Published online by Cambridge University Press:  19 September 2008

Mike Hurley
Mike Hurley
Affiliation:
Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA
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Abstract

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The purpose of this paper is to develop necessary conditions for a diffeomorphism to be topologically stable (lower semistable). Our results combine with a recent theorem of R. Mañé and with earlier results of J. Robbin, C. Robinson, and Z. Nitecki to give a complete characterization of diffeomorphisms of compact manifolds that are both topologically and structurally stable: they are precisely the Axiom A diffeomorphisms that satisfy the strong transversality condition.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 1 , March 1984 , pp. 81 - 88
Copyright
Copyright © Cambridge University Press 1984

References

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