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arXiv · 0801.4948

Trivial centralizers for Axiom A diffeomorphisms

Todd Fisher
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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 $2\leq r\leq \infty$, 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 $Λ$ where $Λ$ is a hyperbolic chain recurrent class for one of the diffeomorphisms.

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Todd Fisher. 2008-01-31. Trivial centralizers for Axiom A diffeomorphisms. https://doi.org/10.1088/0951-7715%2F21%2F11%2F002

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