An open set of structurally unstable families of vector fields in the two-sphere

Yulij Ilyashenko, Yury Kudryashov, Ilya Schurov

Published 2015-06-22Version 1

This is the first part of a two parts paper dedicated to global bifurcations in the plane. In this part we construct an open set of three parameter families whose topological classification has a numerical invariant that may take an arbitrary positive value. In the second part we construct an open set of six parameter families whose topological classification has a functional invariant. Any germ of a monotonically increasing function $(\mathbb R, a) \to (\mathbb R,b)$ for any $a > 0$, $b > 0$ may be realized as this invariant. Here "families" are "families of vector fields in the two-sphere".