Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion

Andres Koropecki, Fabio Armando Tal
2014 Proceedings of the American Mathematical Society  
We construct a C ∞ area-preserving diffeomorphism of the twodimensional 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.
doi:10.1090/s0002-9939-2014-12062-4 fatcat:j2zxergm6fabxg636l4vixc65y