Uniform persistence and repellors for maps

Hofbauer, Josef; So, Joseph W.-H.

doi:10.1090/S0002-9939-1989-0984816-4

Uniform persistence and repellors for maps
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by Josef Hofbauer and Joseph W.-H. So PDF

Proc. Amer. Math. Soc. 107 (1989), 1137-1142 Request permission

Abstract:

We establish conditions for an isolated invariant set $M$ of a map to be a repellor. The conditions are first formulated in terms of the stable set of $M$. They are then refined in two ways by considering (i) a Morse decomposition for $M$, and (ii) the invariantly connected components of the chain recurrent set of $M$. These results generalize and unify earlier persistence results.

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