Trivial centralizers for codimension-one attractors

Abstract

We show that if $\Lambda$ is a codimension-one hyperbolic attractor for a $C^r$ diffeomorphism $f$, where $2\le r\le \infty$, 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 $\Lambda$.

9 pages

Cited by in corpus (3)

• Open sets of diffeomorphisms with trivial centralizer in the $C^1$ topology
• A criterion for the triviality of the centralizer for vector fields and applications
• On the centralizer of vector fields: criteria of triviality and genericity results