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Ω-Stability is not dense in Axiom A

Published online by Cambridge University Press:  19 September 2008

S. E. Patterson
S. E. Patterson
Affiliation:
Northwestern University, Evanston, Illinois, USA
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Abstract

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An example of a diffeomorphism f on a three dimensional manifold M3 is constructed so that f satisfies Axiom A, has a cycle and f has a neighborhood N in Diffr (M3) so that each g in N is not Ω-stable. Existing techniques allow one to extend this example to any compact manifold of dimension greater than two.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 4 , December 1988, pp. 621 - 632
Copyright
Copyright © Cambridge University Press 1988

References

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