Lorenz attractor through saddle-node bifurcations

Abstract

In this paper we consider the unfolding of a geometric Lorenz attractor when the singularity contained in this attractor goes through a saddle-node bifurcation. It is shown that these unfoldings can carry such a geometric Lorenz attractor either directly into a hyperbolic Plykin attractor or into phenomena associated to the unfolding of homoclinic tangencies like for instance strange Henon-like attractors and infinitely many sinks.