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Transverse surfaces and attractors for 3-flows
Author(s):
W.
J.
Colmenarez;
C.
A.
Morales
Journal:
Trans. Amer. Math. Soc.
354
(2002),
795-806.
MSC (2000):
Primary 37Dxx;
Secondary 37C15
Posted:
September 19, 2001
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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:
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
Posted:
September 19, 2001
Additional Notes:
Partially supported by FAPERJ, CNPq and PRONEX of Brasil.
Copyright of article:
Copyright
2001,
American Mathematical Society
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