Preprint A277/2004
Contracting Lorenz attractors through resonant double homoclinic loops

Bernardo San Martim | Morales, Carlos | Pacifico, Maria Jose

**Keywords: **
contracting Lorenz attractors | Lorenz attractor | resonant double homoclinic loops | homoclinic loops

A contracting Lorenz attractor is obtained from the
geometric Lorenz attractor replacing the usual
expanding condition \lambda_3 + \lambda_1 >0
in the eigenvalues \lambda_2 < \lambda_3 < 0 < \lambda_1
at the origin by a {\it {contracting}} condition
\lambda_3 + \lambda_1 <0.
In this paper we analyse the appearence
of contracting Lorenz attractors in the unfolding
of certain resonant double homoclinic loops in dimension three.
We prove that the corresponding unfolding
yields contracting Lorenz attractors in a positive Lebesgue
measure set of parameters, answering a question
posed by Robinson.