Transversal Intersections of invariant manifolds of NMS Flows on S3

Abstract

In this paper NMS flows on S 3 with a round handle decomposition made up of connected sum of tori are considered. We describe these flows from the corresponding filtrations and obtain conditions for the existence of transversal intersections of invariant manifolds of saddle orbits. Moreover, we build the phase portrait for each case in order to obtain a complete description of the flow and to visualize how invariant manifolds of saddles intersect.