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Stability of mixing for toral extensions of hyperbolic systems. (English) Zbl 0988.37034
Proc. Steklov Inst. Math. 216, 350-359 (1997) and Tr. Mat. Inst. Steklova 216, 354-363 (1997).
This paper is devoted to the stability of ergodicity for circle extensions of Anosov diffeomorphisms of a torus. The authors show that a well-known result of Adler, Kitchens and Shub concerning the stability question mentioned above, can be generalized to hyperbolic (or expanding) systems that satisfy a simple cohomological condition and that with this condition a complete analysis of toral extensions is possible. Moreover they give precise conditions for an extension to possess one of three properties: the extension is a) not mixing; b) unstably mixing; c) stably mixing.
For the entire collection see [Zbl 0884.00028].

##### MSC:
 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 37A25 Ergodicity, mixing, rates of mixing