Fat Handles and Phase Portraits of Non Singular Morse-Smale Flows on S3 with Unknotted Saddle Orbits (original) (raw)

Graphs of NMS Flows on S 3 with Knotted Saddle Orbits and No Heteroclinic Trajectories

Acta Mathematica Sinica, English Series, 2007

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. Partially supported by P11B2002-24 (Convenio Bancaixa-Universitat Jaume I) and MTM2004-03244 (MEC) 2 Campos B. and Vindel P.

NMS Flows on S 3 with no Heteroclinic Trajectories Connecting Saddle Orbits

Journal of Dynamics and Differential Equations, 2012

In this paper we find topological conditions for the non existence of heteroclinic trajectories connecting saddle orbits in non singular Morse-Smale flows on S 3 . We obtain the non singular Morse-Smale flows that can be decomposed as connected sum of flows and we show that these flows are those who have no heteroclinic trajectories connecting saddle orbits. Moreover, we characterize these flows in terms of links of periodic orbits.

Visualization of Morse flow with two saddles on 3-sphere diagrams

arXiv (Cornell University), 2022

We describe all possible topological structures of Morse-Smale flows without closed trajectories on a three-dimensional sphere, which have two sources, two sinks, one saddle of Morse index 1, one saddle of Morse index 2, and no more than 10 saddle connections. To classify such flows, a generalized Heegaard diagram or Pr-diagram is used, which in this case consists of a sphere and two closed curves, the intersection points of which correspond to saddle connections. We have found all possible, up to homeomorphism, ways to embed two circles in a 2-sphere with no more than 10 points of transversal intersection and construct its planar visualisations.

Morse Flows with Fixed Points on the Boundary of 3-Manifolds

Journal of Mathematical Sciences

UDC 517.91 We investigate the topological properties, structures, and classifications of the Morse flows with fixed points on the boundary of three-dimensional manifolds. We construct a complete topological invariant of a Morse flow, namely, P r-diagram, which is similar to the Heegaard diagram of a closed three-dimensional manifold.

The topology and dynamics of flows

Open Problems in Topology II, 2007

After a brief survey of various types of flows (Morse-Smale, Smale, Anosov, & partially hyperbolic) we focus on Smale flows on S 3. However, we do give some consideration to Smale flows on other three-manifolds and to Smale diffeomorphisms.