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Proceedings of the American Mathematical Society

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

 

 

On proofs of the $C^0$ general density theorem


Author: Mike Hurley
Journal: Proc. Amer. Math. Soc. 124 (1996), 1305-1309
MSC (1991): Primary 58F08
DOI: https://doi.org/10.1090/S0002-9939-96-03184-X
MathSciNet review: 1307531
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Abstract: We show that if $M$ is a compact manifold, then there is a residual subset ${\mathcal{N}}$ of the set of homeomorphisms on $M$ with the property that if $f\in {\mathcal{N}}$, then the periodic points of $f$ are dense in its chain recurrent set. This result was first announced in [4], but a flaw in that argument was noted in [1], where a different proof was given. It was recently noted in [5] that this new argument only serves to show that the density of periodic points in the chain recurrent set is generic in the closure of the set of diffeomorphisms. We show how to patch the original argument from [4] to prove the result.


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Mike Hurley
Email: mgh3@po.cwru.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03184-X
Keywords: Chain recurrent set, generic homeomorphism
Received by editor(s): October 11, 1994
Communicated by: Mary Rees
Article copyright: © Copyright 1996 American Mathematical Society