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
Full-text PDF
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
