Structures of the flows with a unique singular point on the 2-dimensional disk

2023/04/03 by Alexandr Prishlyak, Prishlyak, Alexandr, Serhii Stas +1
Mathematics · #37c10 #37c15 #37c20 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #G.1.7 #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2304.00751

openalex publication_date 2023/04/03 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28

Abstract

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 code of the flow and have found all possible structures of the flows with no more then 7 sepapratrices.

Related

• Planar graphs as distinguished graph of Morse flows on the 2-disk
• Graph representations of surface flows
• Structure of Morse flows with at most six singular points on the torus with a hole
• Typical one-parameter bifurcations of gradient flows with at most six singular points on the 2-sphere with holes
• Topological structure of optimal flows on the Girl's surface