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Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion

By Andres Koropecki and Fabio Armando Tal


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.Comment: 8 page

Topics: Mathematics - Dynamical Systems, 37E30, 37E45
Year: 2012
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