Trivial centralizers for Axiom A diffeomorphisms

Abstract

We show there is a residual set of non-Anosov $C^{\infty }$ Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. If $M$ is a surface and $2\le r\le \infty$, then we will show there exists an open and dense set of of $C^r$ Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. Additionally, we examine commuting diffeomorphisms preserving a compact invariant set $\Lambda$ where $\Lambda$ is a hyperbolic chain recurrent class for one of the diffeomorphisms.

18 pages

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