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

TL;DR

This paper provides a comprehensive classification of all singular points in generic two-parameter vector field families on compact 2-manifolds, contributing to the broader understanding of bifurcations on the two-sphere.

Contribution

It offers a complete description of singular points in generic 2-parameter vector field families on 2-manifolds, advancing the study of global bifurcations.

Findings

Classification of all possible singular points

Description of bifurcation scenarios on the two-sphere

Framework for analyzing global bifurcations

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.