Groups and Dynamics Seminar

Date: November 2, 2022

Time: 3:00PM - 4:00PM

Location: BLOC 506a

Speaker: Yury Kudriashov, Texas A&M University

Title: Bifurcations of vector fields on the two-sphere

Abstract: A generic vector field on the two-sphere is structurally stable: any other vector field that is sufficiently close to the original one is conjugate to it by a homeomorphism of the sphere. In 1960-s, V. Arnold conjectured that the same is true for a generaic finite parameter family of vector fields on the sphere. Recently, Yu. Ilyashenko, I. Schurov and me disproved this conjecture: we described a locally generic type of a 3-parameter bifurcation such that topological classification of bifurcations of this type has at least one numeric parameter. We also described a 6-parameter bifurcation that have functional moduli of topological classification. I will talk about these examples and their improvements constructed by N. Goncharuk, N. Solodvnikov and me. This talk is an extended version of my talk at the postdoc talks series.