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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Hyperbolicity and cycles

Authors: J. E. Franke and J. F. Selgrade
Journal: Trans. Amer. Math. Soc. 245 (1978), 251-262
MSC: Primary 58F15; Secondary 34C35
MathSciNet review: 511408
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Abstract: In this paper cycle points are defined without the assumption of Axiom A. The closure of the set of cycle points $ \mathcal{C}$ being quasi-hyperbolic is shown to be equivalent to Axiom A plus no cycles. Also we give a sufficient condition for $ \mathcal{C}$ to equal the chain recurrent set. In proving these theorems, a spectral decomposition for quasi-hyperbolic invariant sets is used.

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Keywords: Flows, Axiom A, spectral decomposition, cycle points, chain recurrent, quasi-hyperbolic invariant set
Article copyright: © Copyright 1978 American Mathematical Society