0000000000274248
AUTHOR
Maria José Pacifico
Singular hyperbolic systems
We construct a class of vector fields on 3-manifolds containing the hyperbolic ones and the geometric Lorenz attractor. Conversely, we shall prove that nonhyperbolic systems in this class resemble the Lorenz attractor: they have Lorenz-like singularities accumulated by periodic orbits and they cannot be approximated by flows with nonhyperbolic critical elements.
Global attractors from the explosion of singular cycles
Abstract In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.
On C1 robust singular transitive sets for three-dimensional flows
Abstract The main goal of this paper is to study robust invariant transitive sets containing singularities for C 1 flows on three-dimensional compact boundaryless manifolds: they are partially hyperbolic with volume expanding central direction. Moreover, they are either attractors or repellers. Robust here means that this property cannot be destroyed by small C 1 -perturbations of the flow.