Author:Claude Baesens Publicsh date:2017-07-30 Clicks:

A seminar at Center for Mathematical Sciences, July 31 Monday, at 2:00pmLocation: Center for Mathematical Sciences, Room 813（创新研究院恩明楼813室）speaker: Prof. Claude Baesens, University of Warwick, FRSTitle: SIMPLEST BIFURCATION DIAGRAMS FOR MONOTONE FAMILIES OF VECTOR FIELDS ON A TORUSAbstract: We prove that the bifurcation diagram for a monotone two-parameter family of vector fields on a...

A seminar at Center for Mathematical Sciences, July 31 Monday, at 2:00pm

**Location: **Center for Mathematical Sciences, Room 813（创新研究院恩明楼813室）

**speaker:** Prof. Claude Baesens, University of Warwick, FRS

**Title: **SIMPLEST BIFURCATION DIAGRAMS FOR MONOTONE FAMILIES OF VECTOR FIELDS ON A TORUS

**Abstract: **We prove that the bifurcation diagram for a monotone two-parameter family of vector fields on a torus has to be at least as complicated as the conjectured simplest one proposed in [BGKM1]. To achieve this we define “simplest” by minimising sequentially the numbers of equilibria, Bogdanov-Takens points, closed curves of centre and of neutral saddle, intersections of curves of centre and neutral saddle, Reeb components, other invariant annuli, arcs of rotational homoclinic bifurcation of hori-zontal homotopy type, necklace points, contractible periodic orbits, points of neutral horizontal homoclinic bifurcation and half-plane fan points. We obtain two types of simplest case, including that initially proposed.

**Keywords: **bifurcation, homoclinic bifurcation, rotational homoclinic bifurcation