Trivial centralizers for Axiom A diffeomorphisms

Details Trivial centralizers for Axiom A diffeomorphisms Trivial centralizers for Axiom A diffeomorphisms

2008-01-31

arxiv.org/abs/0801.4948v1

Mathematics

Dynamical Systems

18 pages

Scientific paper

10.1088/0951-7715/21/11/002

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 $\Lambda$ where $\Lambda$ is a hyperbolic chain recurrent class for one of the diffeomorphisms.

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