Dynamical Systems Seminar

I will continue the presentation of my recent work with Mikko Stenlund on periodic pulsatile perturbations of flows that admit weakly stable hyperbolic limit cycles. We show that if shear is present in the unperturbed flow, then sustained, observable chaotic behavior can replace the limit cycle when the system is subjected to a periodic pulsatile drive. In part 1, we stated our main result and introduced a model of linear shear flow. In part 2, we study the simplified linear shear flow model in order to illustrate the geometric ideas behind the main result and highlight the components of its proof.