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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Central Lyapunov exponent of partially hyperbolic diffeomorphisms of $ \mathbb{T}^{3}$


Authors: G. Ponce and A. Tahzibi
Journal: Proc. Amer. Math. Soc. 142 (2014), 3193-3205
MSC (2010): Primary 37-XX; Secondary 37D25, 37D30
Published electronically: June 6, 2014
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Abstract: In this paper we construct some ``pathological'' volume preserving partially hyperbolic diffeomorphisms on $ \mathbb{T}^{3}$ such that their behavior in small scales in the central direction (Lyapunov exponent) is opposite to the behavior of their linearization. These examples are isotopic to Anosov. We also get partially hyperbolic diffeomorphisms isotopic to Anosov (consequently with non-compact central leaves) with zero central Lyapunov exponent at almost every point.


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Additional Information

G. Ponce
Affiliation: Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 13566-590, São Carlos-SP, Brazil
Email: gaponce@icmc.usp.br

A. Tahzibi
Affiliation: Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 13566-590, São Carlos-SP, Brazil
Email: tahzibi@icmc.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12063-6
PII: S 0002-9939(2014)12063-6
Received by editor(s): April 30, 2012
Received by editor(s) in revised form: October 8, 2012
Published electronically: June 6, 2014
Additional Notes: The first-named author is enjoying a doctoral scholarship of FAPESP
The second-named author was supported by CNPq and FAPESP
Communicated by: Nimish Shah
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.