Attractive nonrough limit sets of Lorenz-attractor type

Proofs are presented of results obtained by Afraimovich et al. (1977, 1979) concerning the appearance and structure of Lorenz attractors. The structure of stable limit sets that can arise from Lorenz attractors is considered, with attention given both to the symmetric case and to the general biparametric family. The generation of separatrix loops of periodic motions with negative multipliers is also examined.