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.References
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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
- MR Author ID: 856885
- Email: ak@id.uff.br
- 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
- MR Author ID: 653938
- Email: fabiotal@ime.usp.br
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 3483-3490
- MSC (2010): Primary 37E30, 37E45
- DOI: https://doi.org/10.1090/S0002-9939-2014-12062-4
- MathSciNet review: 3238423