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In this paper we build Non-singular Morse-Smale flows on S 3  with unknotted and unlinked saddle orbits by identifying fat round handles along their boundaries. This way of building the flows enables to get their phase portraits. We also show that the presence of heteroclinic trajectories imposes an order in the round handle decomposition of these flows; this order is total for NMS flows composed of one repulsive, one attractive and n unknotted saddle orbits, for n ≥ 1.

Fat Handles and Phase Portraits of Non Singular Morse-Smale Flows on S 3 with Unknotted Saddle Orbits