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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

$ \Omega $-explosions


Author: J. Palis
Journal: Proc. Amer. Math. Soc. 27 (1971), 85-90
MSC: Primary 57.50; Secondary 34.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0270400-3
MathSciNet review: 0270400
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Abstract: In the present paper it is shown that if a flow satisfies Smale's Axiom $ {\text{A'}}$ and there is a cycle on its nonwandering set $ \Omega $, then the flow is not $ \Omega $-stable. This is done by ``blowing up'' the nonwandering set with a small perturbation. It is possible, in this setting, to give a characterization of $ \Omega $-stable flows when the nonwandering set is the union of a finite number of critical elements.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0270400-3
Keywords: Nonwandering set $ \Omega $, $ \Omega $-conjugate, $ \Omega $-stable, Smale's Axiom $ {\text{A'}}$, cycle property of $ \Omega $, characterization of $ \Omega $-stability
Article copyright: © Copyright 1971 American Mathematical Society