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arXiv · 1206.2409

Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion

Andres Koropecki·Fabio Armando Tal
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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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Andres Koropecki, Fabio Armando Tal. 2012-06-11. Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion. https://doi.org/10.1090/s0002-9939-2014-12062-4

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