Nearly 100 years ago, van der Pol and van der Mark observed that irregularities developed when certain electric circuits with stable oscillations were periodically forced. Their work stimulated many analytical studies, from Cartwright \& Littlewood (1945), Levinson (1949) to Levi (1981) and Haiduc (2009). Much was learned along the way, but a complete analytical understanding of the forced van der Pol oscillator has remained illusive. In this talk, I will discuss a related model that is more amenable to analysis: Consider an arbitrary dynamical system with a limit cycle. To this system, periodic ``kicks'' (or forcings turned on for short durations) are interspersed with longer relaxation times during which the system is allowed to restore itself. To demonstrate the dynamical richness of these models, I will use an especially simple example, the linear shear flow in 2D, in which one can see clearly how the dynamical picture is controlled by a quantity proportional to shear and kick amplitude and inversely proportional to damping. Increasing this quantity gradually, one observes first invariant curves, then the breaking of invariant curves (a dissipative version of KAM), followed by the development of horseshoes and sinks, and eventually ``strange attractors” with observable chaos.
Freitag, den 27. Oktober 2017 um 15.00-16.00 Uhr, in Mathematikon, INF 205, Konferenzraum, 5. OG Freitag, den 27. Oktober 2017 at 15.00-16.00, in Mathematikon, INF 205, Konferenzraum, 5. OG
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. P. Albers