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Working paper

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

arxiv.org. math. Cornell University, 2015. No. 1506.06797.
Ilyashenko Y., Kudryashov Y., Schurov I.
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 may be realized as this invariant. Here "families" are "families of vector fields in the two-sphere".