Trivial centralizers for codimension-one attractors

Details Trivial centralizers for codimension-one attractors Trivial centralizers for codimension-one attractors

2008-06-05

arxiv.org/abs/0806.0991v1

Mathematics

Dynamical Systems

9 pages

Scientific paper

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

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