Centralizers of Anosov diffeomorphisms on tori.

*(English)*Zbl 0675.58029For a diffeomorphism f on a smooth compact connected manifold M we say that f has a trivial centralizer, if the only diffeomorphisms on M commuting with f have the form ${f}^{m}$, $m\in \mathbb{Z}$. The authors prove that for an open and dense subset of Anosov diffeomorphisms of the n-dimensional torus the centralizer is trivial.

In a previous paper the authors [ibid. 22, No.1, 81-98 (1989)] consider sets of diffeomorphisms with trivial centralizers on arbitrary compact connected manifolds.

Reviewer: L.N.Stoyanov

##### MSC:

37D99 | Dynamical systems with hyperbolic behavior |