arXiv subjects

Maria Loseva

Publications and source records attributed to Maria Loseva.

4 recordsLinked to original sources

arXiv2024

Structure of the codimesion one gradient flows with at most six singular points on the M\"obius strip

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 diagrams of flows. The saddle-node bifurcation is specified by selecting a separatrix in the diagram of the Morse flow befor the bifurcation and the saddle connection is specified by a separatrix, which connect two saddles on the diagram.

math.DS↗

arXiv2024

Structure of Morse flows with at most six singular points on the torus with a hole

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, we use separatrix diagrams of flows. The saddle-node bifurcation is specified by selecting a separatrix in the separatrix diagram of the flow befor the bifurcation.

math.DS↗

arXiv2023

Typical one-parameter bifurcations of gradient flows with at most six singular points on the 2-sphere with holes

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 of flows. The saddle-node singularity is specified by selecting a separatrix in the diagram of the flow befor the bifurcation and the saddle connection is specified by a separatrix, which conect two saddles.

math.DS↗

arXiv2022

Topological structure of optimal flows on the Girl's surface

We investigate the topological structure of flows on the Girl's surfaces which is one of two possible immersions of the projective plane in three-dimensional space with one triple point of the selfintersection. First, we describe the cellular structure of the Boy's and Girl's surfaces and prove that there are unique images of the project plane in the form of a 2-disc, in which the opposite points of the boundary are identified and this boundary belongs to the preimage of the 1-skeleton of the surface. Second, we described three structures of flows with one fixed point and no separatrix on the Girl's surface and proved that there are no other such flows. Third, we proved that Morse-Smale flows and they alone are structurally stable on the Boy's and Girl's surfaces. Fourth, we have found all possible structures of optimal Morse-Smale flows on the Girl's surface. Fifth, we have obtained a classification of Morse-Smale flows on the projective plane, that immersed on the Girl's surface. And finally, we described the components of linear connectivity of sets of these flows

math.DS↗