Nonsingular structurally stable chaotic 3-flows of attractor–repeller type

We show that any orientable closed 3-manifold M admits structurally stable non-singular flow f t whose non-wandering set NW(f t) consists of a two-dimensional expanding attractor and finitely many repelling periodic trajectories. For M=S3, we prove that the set of repelling periodic trajectories can be an arbitrary link provided that this link contains the figure-eight knot. When a link consists of a unique repelling periodic trajectory (not necessarily a figure-eight knot), we prove that this trajectory cannot be a torus knot. For any closed 3-manifold M, we show that if l is a closed repelling periodic trajectory of structurally stable non-singular flow f t whose non-wandering set NW(f t) consists of a two-dimensional expanding attractor and l, then l is not a trivial knot (i.e., l does not bound an embedded disk in M).