Singular hyperbolic systems

Morales, C.; Pacifico, M.; Pujals, E.

doi:10.1090/S0002-9939-99-04936-9

Singular hyperbolic systems
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by C. A. Morales, M. J. Pacifico and E. R. Pujals

Proc. Amer. Math. Soc. 127 (1999), 3393-3401

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

Published electronically: May 4, 1999

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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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