The dynamics of perturbations of the contracting Lorenz attractor

  • Alvaro Rovella
Article

DOI: 10.1007/BF01237679

Cite this article as:
Rovella, A. Bol. Soc. Bras. Mat (1993) 24: 233. doi:10.1007/BF01237679

Abstract

We show here that by modifying the eigenvalues λ2 < λ3 < 0 < λ1 of the geometric Lorenz attractor, replacing the usualexpanding condition λ31 > 0 by acontracting condition λ31 < 0, we can obtain vector fields exhibiting transitive non-hyperbolic attractors which are persistent in the following measure theoretical sense: They correspond to a positive Lebesgue measure set in a twoparameter space. Actually, there is a codimension-two submanifold in the space of all vector fields, whose elements are full density points for the set of vector fields that exhibit a contracting Lorenz-like attractor in generic two parameter families through them. On the other hand, for an open and dense set of perturbations, the attractor breaks into one or at most two attracting periodic orbits, the singularity, a hyperbolic set and a set of wandering orbits linking these objects.

Copyright information

© Sociedade Brasileira de Matemática 1993

Authors and Affiliations

  • Alvaro Rovella
    • 1
  1. 1.Fac. IngeneriaIMERLMontevideoUruguay

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