Dynamics Seminar

Event Information Global bifurcations of planar vector fields
15:10 on Monday September 16, 2019
16:00 on Monday September 16, 2019
BA6183, Bahen Center, 40 St. George St.
Yury Kudryashov

University of Toronto

While generic vector fields on S² are structurally stable, locally generic three-parameter families of vector fields on S² can be structurally unstable, i.e. locally generic close families experience topologically different bifurcations. This effect was recently discovered by Yu. Ilyashenko, I. Schurov, and the speaker.

It seems natural to ask how far can finite-parameter families fall from being structurally stable: can the classification have multiple numerical invariants? functional invariants? do these invariants survive if we add more parameters?

I will discuss some examples showing that finite-parameter families can be *very* far from being structurally stable. The talk is based on a joint work with Yu. Ilyashenko, I. Schurov, N. Goncharuk, and N. Solodovnikov.