*
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