Transversal intersections of invariant manifolds of NMS flows on $S^{3}$

Abstract

In this paper NMS flows on $S^{3}$ with a round handle decomposition made upof connected sum of tori are considered. We describe these flows from thecorresponding filtrations and obtain conditions for the existence oftransversal intersections of invariant manifolds of saddle orbits.  &nbsp Moreover, we build the phase portrait for each case in order to obtain acomplete description of the flow and to visualize how invariant manifolds ofsaddles intersect.