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Graphs of NMS flows on \(S^{3}\) with knotted saddle orbits and no heteroclinic trajectories. (English) Zbl 1137.37312

Summary: We consider NMS systems on \(S^{3}\) without heteroclinic trajectories connecting two saddles orbits and we build the dual graphs associated with this kind of flows. We prove that flows coming from essential attachments of orientable round 1-handles can be reproduced from the corresponding dual graph.

MSC:

37D15 Morse-Smale systems
37A20 Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations
57M25 Knots and links in the \(3\)-sphere (MSC2010)
37E25 Dynamical systems involving maps of trees and graphs
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