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

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.

8 pages, to appear in Proc. Amer. Math. Soc

References in corpus (1)

• Transitivity of Surface Dynamics Lifted to Abelian Covers

Cited by in corpus (6)

• Strictly Toral Dynamics
• On annular maps of the torus and sublinear diffusion
• Bounded and unbounded behavior for area-preserving rational pseudo-rotations
• Rotational deviations and invariant pseudo-foliations for periodic point free torus homeomorphisms
• Periodic point free homeomorphisms and irrational rotation factors
• Infinite ergodic theory and Non-extensive entropies