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Transactions of the American Mathematical Society

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



$\Omega $-inverse limit stability theorem

Author: Hiroshi Ikeda
Journal: Trans. Amer. Math. Soc. 348 (1996), 2183-2200
MSC (1991): Primary 58F10; Secondary 58F15
MathSciNet review: 1355074
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Abstract: We prove that if an endomorphism $f$ satisfies weak Axiom A and the no-cycles condition then $f$ is $\Omega $-inverse limit stable. This result is a generalization of Smale's $\Omega $-stability theorem from diffeomorphisms to endomorphisms.

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Hiroshi Ikeda
Affiliation: Department of Mathematics, School of Education, Waseda University, Shinjuku, Tokyo, 169-50, Japan

Keywords: Inverse limit stability, weak Axiom A, prehyperbolic sets
Received by editor(s): November 12, 1993
Received by editor(s) in revised form: July 18, 1994
Dedicated: Dedicated to the memory of my father
Article copyright: © Copyright 1996 American Mathematical Society