10 papers · 1 filter
Algorithms and topological invariants for dynamic systems. II. Discrete Structures
Alexandr Prishlyak
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equi…
Algorithms and topological invariants for dynamic systems. I. Basic definitions
Alexandr Prishlyak
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equi…
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…
Structure of the codimesion one gradient flows with at most six singular points on the Möbius strip
Maria Loseva, Alexandr Prishlyak, Kateryna Semenovych +1
We describe all possible topological structures of Morse flows and typical one-parametric gradient bifurcation on the Möbius strip in the case that the number of singular point of…
Structure of Morse flows with at most six singular points on the torus with a hole
Maria Loseva, Alexandr Prishlyak, Kateryna Semenovych +1
We describe all possible topological structures of Morse flows and typical gradient saddle-nod bifurcation of flows on the 2-dimensional torus with a hole in the case that the numb…
Structures of the flows with a unique singular point on the 2-dimensional disk
Alexandr Prishlyak, Serhii Stas
We investigate topological propeties of flows with one singular point and without closed orbits on the 2-dimensional disk. To classify such flows, destingueshed graph is used, whic…