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Bulletin of the London Mathematical Society Advance Access originally published online on December 10, 2008
Bulletin of the London Mathematical Society 2009 41(1):51-56; doi:10.1112/blms/bdn100
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© 2008 London Mathematical Society

Trivial centralizers for codimension-one attractors

Todd Fisher

Department of Mathematics
Brigham Young University
Provo, UT 84602
USA

Received 3 June 2008. Accepted 21 August 2008.

We show that if {Lambda} is a codimension-one hyperbolic attractor for a Cr diffeomorphism f, where 2 ≤ r ≤ {infty}, and f is not Anosov, then there is a neighborhood U of f in Diffr(M) and an open and dense set V of U such that any g isin V has a trivial centralizer on the basin of attraction for {Lambda}.

2000 Mathematics Subject Classification 37C05 (primary), 37C20, 37C29, 37D05, 37D20 (secondary).


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