On proofs of the general density theorem
Author:
Mike Hurley
Journal:
Proc. Amer. Math. Soc. 124 (1996), 13051309
MSC (1991):
Primary 58F08
MathSciNet review:
1307531
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Abstract: We show that if is a compact manifold, then there is a residual subset of the set of homeomorphisms on with the property that if , then the periodic points of 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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Additional Information
Mike Hurley
Email:
mgh3@po.cwru.edu
DOI:
http://dx.doi.org/10.1090/S000299399603184X
PII:
S 00029939(96)03184X
Keywords:
Chain recurrent set,
generic homeomorphism
Received by editor(s):
October 11, 1994
Communicated by:
Mary Rees
Article copyright:
© Copyright 1996
American Mathematical Society
