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

 

Transverse surfaces and attractors for 3-flows


Authors: W. J. Colmenarez and C. A. Morales
Journal: Trans. Amer. Math. Soc. 354 (2002), 795-806
MSC (2000): Primary 37Dxx; Secondary 37C15
Published electronically: September 19, 2001
MathSciNet review: 1862568
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Abstract: We prove that a hyperbolic strange attractor of a three-dimensional vector field is a suspension if it exhibits a transverse surface over which the unstable manifold induces a lamination without closed leaves. We also study the topological equivalence of singular attractors exhibiting transverse surfaces for three-dimensional vector fields.


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Additional Information

W. J. Colmenarez
Affiliation: Instituto de Matematica, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, Brazil
Address at time of publication: Universidad Centroccidental Lizandro Alvarado, Departamento de Matemática, Decamato de Ciencias, Apdo 400, Barquisimeto, Venezuela
Email: wilmerc@pg.im.ufrj.br

C. A. Morales
Affiliation: Instituto de Matematica, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, Brazil
Email: morales@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02822-7
PII: S 0002-9947(01)02822-7
Keywords: Anosov flow, hyperbolicity, cross-section
Received by editor(s): October 27, 1999
Received by editor(s) in revised form: November 15, 2000
Published electronically: September 19, 2001
Additional Notes: Partially supported by FAPERJ, CNPq and PRONEX of Brasil.
Article copyright: © Copyright 2001 American Mathematical Society