Hyperbolicity and cycles

Franke, J. E.; Selgrade, J. F.

doi:10.1090/S0002-9947-1978-0511408-0

Hyperbolicity and cycles
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by J. E. Franke and J. F. Selgrade PDF

Trans. Amer. Math. Soc. 245 (1978), 251-262 Request permission

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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The gradient structure of a flow

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