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

 

Singular hyperbolic systems


Authors: C. A. Morales, M. J. Pacifico and E. R. Pujals
Journal: Proc. Amer. Math. Soc. 127 (1999), 3393-3401
MSC (1991): Primary 58F10, 58F15
Published electronically: May 4, 1999
MathSciNet review: 1610761
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Abstract: We construct a class of vector fields on 3-manifolds containing the hyperbolic ones and the geometric Lorenz attractor. Conversely, we shall prove that nonhyperbolic systems in this class resemble the Lorenz attractor: they have Lorenz-like singularities accumulated by periodic orbits and they cannot be approximated by flows with nonhyperbolic critical elements.


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Additional Information

C. A. Morales
Affiliation: Université de Bourgogne, Laboratoire de Topologie, B.P.400, 21011, Dijon Cedex-France
Address at time of publication: Instituto de Matemàtica, Universidade Federal do Rio de Janeiro, C.P. 68.530, CEP 21.945-970, Rio de Janeiro, Brazil
Email: cmorales@u-bourgogne.fr, morales@impa.br

M. J. Pacifico
Affiliation: Instituto de Matemàtica, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, Brazil
Email: pacifico@impa.br

E. R. Pujals
Email: enrique@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04936-9
PII: S 0002-9939(99)04936-9
Keywords: Lorenz attractor, hyperbolicity, Axiom A
Received by editor(s): November 24, 1997
Received by editor(s) in revised form: January 22, 1998
Published electronically: May 4, 1999
Additional Notes: This work was partially supported by CNPq-Brasil, Faperj-Brasil, Pronex-Brasil. The first author was partially supported by CNRS-France.
Communicated by: Mary Rees
Article copyright: © Copyright 1999 American Mathematical Society