7 papers
Morse functions with four critical points on immersed 2-spheres
Svitlana Bilun, Bohdana Hladysh, Alexandr Prishlyak +1
We investigate topological properties of simple Morse functions with 4 critical points on immersed 2-spheres. To classify such functions, dual graph of immersion and Reeb graphs is…
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…
Typical one-parameter bifurcations of gradient flows with at most six singular points on the 2-sphere with holes
Svitlana Bilun, Maria Loseva, Olena Myshnova +1
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…
Gradient vector fields of codimension one on the 2-sphere with at most ten singular points
Svitlana Bilun, Bohdana Hladysh, Alexandr Prishlyak +1
We describe all possible topological structures of codimension one gradient vector fields on the shpere with at most ten singular points. To describe structures, we use a graph who…
Structures of optimal discrete gradient vector fields on surface with one or two critical cells
Svitlana Bilun, Maria Hrechko, Olena Myshnova +1
We describe all possible structures of discrete vector field (discrete Morse functions) with minimal number of critical cells on the regular CW-complex for the 2-disk (1 cell), the…
Topological structure of Morse functions on the projective plane
Svitlana Bilun, Alexandr Prishlyak, Serhii Stas +1
To investigate the topological structure of Morse functions on the projective plane we use the Reeb graphs. We describe it properties and prove that it is a complete topological in…