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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

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

E. R. Pujals

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