Proceedings of the American Mathematical Society

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



Uniform persistence and repellors for maps

Authors: Josef Hofbauer and Joseph W.-H. So
Journal: Proc. Amer. Math. Soc. 107 (1989), 1137-1142
MSC: Primary 58F12; Secondary 58F40, 92A15
MathSciNet review: 984816
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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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Keywords: Discrete semi-dynamical systems, permanence, uniform persistence, repellor, isolated invariant set, Morse decomposition, chain recurrent set, basic sets, average Lyapunov functions, global attractor
Article copyright: © Copyright 1989 American Mathematical Society