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Centralizers of Anosov diffeomorphisms on tori. (English) Zbl 0675.58029

For 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. 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:
37D99Dynamical systems with hyperbolic behavior