Topology of optimal flows with collective dynamics on closed orientable surfaces
Alexandr Prishlyak, Mariya Viktorovna Loseva
Abstract
We consider flows on a closed surface with one or more heteroclinic cycles that divide the surface into two regions. One of the region has gradient dynamics, like Morse fields. The other region has Hamiltonian dynamics generated by the field of the skew gradient of the simple Morse function. We construct the complete topological invariant of the flow using the Reeb and Oshemkov-Shark graphs and study its properties. We describe all possible structures of optimal flows with collective dynamics on oriented surfaces of genus no more than 2, both for flows containing a center and for flows without it.
Topics & Concepts
SkewMathematicsInvariant (physics)Balanced flowSurface (topology)Topology (electrical circuits)Morse codeMorse theoryFlow (mathematics)Pure mathematicsMathematical analysisGeometryComputer scienceCombinatoricsMathematical physicsTelecommunicationsMathematical Dynamics and FractalsTopological and Geometric Data AnalysisStochastic processes and statistical mechanics