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Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion

Authors: Andres Koropecki and Fabio Armando Tal
Journal: Proc. Amer. Math. Soc. 142 (2014), 3483-3490
MSC (2010): Primary 37E30, 37E45
Published electronically: June 19, 2014
MathSciNet review: 3238423
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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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Additional Information

Andres Koropecki
Affiliation: Instituto de Matemática e Estatística, Universidade Federal Fluminense, Rua Mário Santos Braga S/N, 24020-140 Niteroi, RJ, Brazil

Fabio Armando Tal
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090 São Paulo, SP, Brazil

Received by editor(s): July 11, 2012
Received by editor(s) in revised form: September 14, 2012, October 1, 2012, and October 11, 2012
Published electronically: June 19, 2014
Additional Notes: The first author was partially supported by CNPq-Brasil.
The second author was partially supported by FAPESP and CNPq-Brasil
Communicated by: Nimish Shah
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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