Topology of optimal flows with collective dynamics on closed orientable surfaces

Topology of optimal flows with collective dynamics on closed orientable surfaces

Blog Article

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 Sponge generated by the field of the skew gradient of the simple Morse function.

We construct Interior Parts 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.