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arXiv · 0902.2474

A mixing-like property and inexistence of invariant foliations for minimal diffeomorphisms of the 2-torus

Alejandro Kocsard·Andres Koropecki
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Abstract

We consider diffeomorphisms in the $C^\infty$-closure of the conjugancy class of translations of the 2-torus. By a theorem of Fathi and Herman, a generic diffeomorphism in that space is minimal and uniquely ergodic. We define a new mixing-like property, which takes into account the "directions" of mixing, and we prove that generic elements of the space in question satisfy this property. As a consequence, we show that there is a residual set of strictly ergodic diffeomorphisms without invariant foliations of any kind. We also obtain an analytic version of these results.

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Alejandro Kocsard, Andres Koropecki. 2009-02-14. A mixing-like property and inexistence of invariant foliations for minimal diffeomorphisms of the 2-torus. https://doi.org/10.1090/s0002-9939-09-09903-1

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