Singular points in generic two-parameter families of vector fields on 2-manifold

2024/10/15 by D. A. Filimonov, Filimonov, Dmitry A., Yu. Ilyashenko +1 · 1 citation
Computer Science · Mathematics · #34C23 (Secondary) #37G10 (Primary) 58K45 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.11465

openalex publication_date 2024/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a full description of all possible singular points that occur in generic 2-parameter families of vector fields on compact 2-manifolds. This is a part of a large project aimed to a complete study of global bifurcations in two-parameter families of vector fields on the two-sphere.

Cited by

• Disconnected large bifurcation supports and Cartesian products of bifurcations

Related

• Dynamics of generic 1-parameter perturbations of a vector field with a singular point of codimension k
• Generic 2-parameter perturbations of parabolic singular points of vector\n fields in C
• Vector fields with a given set of singular points
• Generic singularities of line fields on 2D manifolds
• Sparkling saddle loops of vector fields on surfaces