Yulij Ilyashenko (Independent University of Moscow)

First steps of the global bifurcation theory on the two sphere

This talk presents the development of the theory named in the title, during the last three years. Bifurcations in generic one-parameter families were classified; the answer appeared to be quite unexpected.

An important and non-trivial question "who bifurcates?" was answered. A countable and even continuous number of topologically non-equivalent germs of bifurcation diagrams was found. Various structurally unstable three-parameter families were constructed.

These are joint results of the speaker and his collaborators: N. Goncharuk, D. Filimonov, Yu. Kudryashov, N. Solodovnikov, I. Schurov and others. Some open problems will be stated.