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math.DS2026
Complete Topological Invariant and Coding of Homoclinic Flows on the Two-Dimensional Sphere
Alexandr Prishlyak, Illia Ovtsynov
We study codimension one homoclinic flows on closed surfaces and introduce a complete topological invariant based on the structural graph of the flow and the distinguishing graphs…
math.DS2026
The structure of Morse flows and co-dimension one gradient flows on the sphere with holes
Illia Ovtsynov, Alexandr Prishlyak
We describe all possible topological structures of typical one-parameter bifurcations of gradient flows on the 2-sphere with holes in the case that the number of singular point of…
math.DS2024
Structure of optimal gradient flows bifurcations on closed surfaces
Illia Ovtsynov, Alexandr Prishlyak
We consider structure of typical gradient flows bifurcations on closed surfaces with minimal number of singular points. There are two type of such bifurcations: saddle-node (SN) an…