  The algebraic structure of the attractors in a dynamical system determine
much of its global dynamics. The collection of all attractors has a natural
lattice structure, and this structure can be detected through attracting
neighborhoods, which can in principle be computed. Indeed, there has been much
recent work on developing and implementing general computational algorithms for
global dynamics, which are capable of computing attracting neighborhoods
efficiently. Here we address the question of whether all of the algebraic
structure of attractors can be captured by these methods.
