Speaker: Prof.Xu Zhang（Shandong University）

Title: A geometric criterion for the existence of chaos based on periodic orbits in continuous-time autonomous systems

Time: Fri, Oct.25 2019,AM:09:00-11:30

Location: Room 4318, Building No.4, Wushan Campus

Abstract：

     In this talk, a new geometric criterion is introduced for the existence of chaos in continuous-time autonomous systems in three-dimensional Euclidean spaces: the intersection of stable and unstable manifolds of two points on a hyperbolic periodic orbit implies the existence of a Smale horseshoe in a subshift of finite type on cross-sections of these two points. This criterion is based on the existence of a hyperbolic periodic orbit, differing from the classical equilibrium-based Shilnikov criterion and the condition of transversal homoclinic or heteroclinic orbits of Poincare maps.