Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion

Koropecki, Andres; Tal, Fabio

doi:10.1090/S0002-9939-2014-12062-4

Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion
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by Andres Koropecki and Fabio Armando Tal PDF

Proc. Amer. Math. Soc. 142 (2014), 3483-3490 Request permission

Abstract:

We construct a $C^\infty$ area-preserving diffeomorphism of the two-dimensional torus which is Bernoulli (in particular, ergodic) with respect to Lebesgue measure, homotopic to the identity, and has a lift to the universal covering whose rotation set is $\{(0,0)\}$, which in addition has the property that almost every orbit by the lifted dynamics is unbounded and accumulates in every direction of the circle at infinity.

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