Large bifurcation supports

• 主讲人：Prof. Yulij Ilyashenko
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2022-05-05 21:00 - 2022-05-05 22:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/BBD59D040E4E91A35EFFC9E42CEF593A
Valid Until: 2026-06-30 23:59

 

Abstract:  The talk deals with a general problem of the bifurcation theory on the two-sphere. Consider a vector field with arbitrary degeneracies: complex singular points, multiple limit cycles and polycycles. What part of the phase portrait will bifurcate under a perturbation of this field, and what part will remain unchanged? Not only the degenerated parts of the phase portrait mentioned above will bifurcate; but some generic parts will also. A highly nontrivial question arises: WHO BIFURCATES? The answer will be given in the talk based on joint work with Natalya Goncharuk.

 

Bio: Prof. Yulij Ilyashenko is one of the most renowned Russian scientists working in Differential Equations, Dynamical Systems and Geometry. He obtained a big number of brilliant results in bifurcation theory and dynamics beyond uniform hyperbolicity. In particular, he proved the finiteness of the number of limit cycles for polynomial vector fields, thus giving a partial solution to Hilbert's 16^th problem (the previous proof provided by Dulac contained a serious gap).
    Yulij Sergeevich Ilyashenko is the Rector of the Independent University of Moscow, vice-president of Moscow Mathematical Society, and Professor at Moscow State University, Cornell University, Higher School of Economics, and Steklov Mathematical Institute. Besides, Prof. Ilyuashenko is a member of the editorial boards of several prestigious journals including Ergodic Theory and Dynamical Systems, Journal of Dynamics and control systems and Main Editor of Moscow Mathematical Journal.