Ω-explosions

Palis, J.

doi:10.1090/S0002-9939-1971-0270400-3

$\Omega$-explosions
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Proc. Amer. Math. Soc. 27 (1971), 85-90 Request permission

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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