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

DOI:
https://doi.org/10.1090/S0002-9939-99-04936-9

Published electronically:
May 4, 1999

MathSciNet review:
1610761

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-99-04936-9

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