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arXiv · 1405.1492

Open sets of diffeomorphisms with trivial centralizer in the $C^1$ topology

Lennard Bakker·Todd Fisher
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Abstract

On the torus of dimension $2$, $3$, or $4$, we show that the subset of diffeomorphisms with trivial centralizer in the $C^1$ topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to obtain trivial centralizer for an open neighbourhood of Anosov diffeomorphisms arbitrarily near certain irreducible hyperbolic toral automorphism.

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Lennard Bakker, Todd Fisher. 2014-05-07. Open sets of diffeomorphisms with trivial centralizer in the $C^1$ topology. https://doi.org/10.1088/0951-7715%2F27%2F12%2F2869

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