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.

Anexos:

• mps6.pdf