## ABSTRACT

This chapter describes the geometry of the Lorenz attractor in terms of a yoke of outsets from distinguished organizers, and focuses on the generalization of this outstructure to other chaotic attractors. Two basic sets of a flow, Alpha and Omega, are considered. Thus, some trajectory has Alpha for its alpha limit set and Omega for its omega limit set. Due to the hyperbolic structure of the critical elements, the closure of the union of the three outsets is locally attractive. It is a candidate for an attractor, in fact. The omega limit sets in the boundary of these outsets are also yoked. We will see that these yokes can behave very much like homoclinic cycles in some flows: in the presence of reinsertion, they may make horseshoes, knots, and chaos. Considering the implications of the hyperbolicity of Omega, and the invariant manifold theorem, there must be an intersection of the boundary of Out(A) with Out(Y) itself.