The complement of the stable manifold for one-dimensional endomorphisms

Arteaga, Carlos

doi:10.1090/S0002-9939-1987-0884481-9

The complement of the stable manifold for one-dimensional endomorphisms
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Proc. Amer. Math. Soc. 100 (1987), 367-370 Request permission

Abstract:

Let $N$ denote either the circle ${S^1}$ or the closed interval $I = [0,1]$ and let $f$ be a ${C^1}$ endomorphism of $N$. Let $\Sigma (f)$ be the complement of the union of the stable manifolds of the sinks of $f$. In this paper we give necessary and sufficient conditions for $\Sigma (f)$ to consist of eventually periodic points.

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