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Proceedings of the American Mathematical Society

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

 

 

The complement of the stable manifold for one-dimensional endomorphisms


Author: Carlos Arteaga
Journal: Proc. Amer. Math. Soc. 100 (1987), 367-370
MSC: Primary 58F12; Secondary 54H20, 58F20
DOI: https://doi.org/10.1090/S0002-9939-1987-0884481-9
MathSciNet review: 884481
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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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DOI: https://doi.org/10.1090/S0002-9939-1987-0884481-9
Article copyright: © Copyright 1987 American Mathematical Society