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

DOI:
https://doi.org/10.1090/S0002-9947-04-03706-7

Published electronically:
December 10, 2004

MathSciNet review:
2159702

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show nonuniform hyperbolicity for a class of attractors of 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:
https://doi.org/10.1090/S0002-9947-04-03706-7

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.