Attractors for return maps near homoclinic tangencies of three-dimensional dissipative diffeomorphisms

Abstract

We numerically analyse different kinds of one-dimensional and two-dimensional attractors for the limit return map associated to the unfolding of homoclinic tangencies for a large class of three-dimensional dissipative diffeomorphisms. Besides describing the topological properties of these attractors, we often numerically compute their Lyapunov exponents in order to clarify where two-dimensional strange attractors can show up in the parameter space. Hence, we are specially interested in the case in which the unstable manifold of the periodic saddle taking part in the homoclinic tangency has dimension two.