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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nonuniform hyperbolicity for singular hyperbolic attractors


Author: Wilmer J. Colmenárez Rodriguez
Journal: Trans. Amer. Math. Soc. 357 (2005), 4131-4140
MSC (2000): Primary 37Dxx; Secondary 37C15
Published electronically: December 10, 2004
MathSciNet review: 2159702
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Abstract: In this paper we show nonuniform hyperbolicity for a class of attractors of $C^2$ flows in dimension three. These attractors are partially hyperbolic with central direction being volume expanding, contain dense periodic orbits and hyperbolic singularities of the associated vector field. Classical expanding Lorenz attractors are the main examples in this class.


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Additional Information

Wilmer J. Colmenárez Rodriguez
Affiliation: Departamento de Matemática, Decanato de Ciencias y Tecnología, Universidad Centro Occidental Lisandro Alvarado, Apartado 400 Barquisimeto, Venezuela
Email: wilmerc@uicm.ucla.edu.ve

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03706-7
PII: S 0002-9947(04)03706-7
Keywords: Nonuniform hyperbolicity, singular attractors, 3-flows
Received by editor(s): June 17, 2003
Received by editor(s) in revised form: December 2, 2003
Published electronically: December 10, 2004
Additional Notes: This work was partially supported by FONACIT and CDCHT-UCOLA (Venezuela) and by CNPq (Brazil)
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.