Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Prishlyak, Alexandr"'
Autor:
Ovtsynov, Illia, Prishlyak, Alexandr
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) and saddle connections (SC). The structure of a bifurcation is determina
Externí odkaz:
http://arxiv.org/abs/2408.10687
We describe all possible topological structures of Morse flows and typical one-parametric gradient bifurcation on the M\"obius strip in the case that the number of singular point of flows is at most six. To describe structures, we use the separatrix
Externí odkaz:
http://arxiv.org/abs/2404.07233
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 number of singular point of flows is at most six. To describe structures,
Externí odkaz:
http://arxiv.org/abs/2404.02223
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 used. We have found all possible structures of the functions:6 struct
Externí odkaz:
http://arxiv.org/abs/2304.04392
Autor:
Prishlyak, Alexandr, Stas, Serhii
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, which is a two-colored rooted tree imbedded in the plane. We construct a c
Externí odkaz:
http://arxiv.org/abs/2304.00751
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 flows is at most six. To describe structures, we separatrix diagrams o
Externí odkaz:
http://arxiv.org/abs/2303.14975
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 whose edges are one-dimensional stable manifolds. The saddle-node singula
Externí odkaz:
http://arxiv.org/abs/2303.10929
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 2-sphere (2 cells), the cylinder (2 cells) and Mobius band (2 cells).
Externí odkaz:
http://arxiv.org/abs/2303.07258
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 invariant of simple Morse function on $\mathbb{R} P^2$. We prove recuren
Externí odkaz:
http://arxiv.org/abs/2303.03850
Autor:
Bilun, Svitlana, Prishlyak, Alexandr
We describe all possible topological structures of Morse-Smale flows without closed trajectories on a three-dimensional sphere, which have two sources, two sinks, one saddle of Morse index 1, one saddle of Morse index 2, and no more than 10 saddle co
Externí odkaz:
http://arxiv.org/abs/2209.12174