Research topics
Quasiperiodically forced systems Quasiperiodic forcing is the simplest type of aperiodic driving that can occur in dynamical systems. In the modelling of realworld phenomena, it comes up whenever the process in question is influenced by two or more periodic external factors with incommensurate frequencies. Examples are multifrequency forced oscillators or electric circuits and Schrödinger operators with quasiperiodic potential. One phenomenon which has attracted particular interest in qpf systems is the widespread occurrence of socalled strange nonchaotic attractors (SNA). These objects combine a complicated structure with nonchaotic dynamics, a combination which is quite rare in dynamical systems otherwise. Another interesting aspect of qpf 1Dmaps is that they can be considered either as 1D nonautonomous systems or as autonomous 2Dmaps with a special skew product structure. In both situations, they can serve as simple models whose study allows to obtain further insights about the general case. 

Nonautonomous bifurcation theory One of the primary goals of nonautonomous bifurcation theory is the description of nonautonomous counterparts of the classical bifurcation pattern of dynamical systems. The external forcing often leads to qualitative changes of the bifurcation scenario. For example, saddlenode bifurcations may become nonsmooth (thus involving strange nonchaotic attractors) and the usual Hopf bifurcation pattern gives way to the twostep scenario for the nonautonomous Hopf bifurcation proposed by Ludwig Arnold. 

Dynamics of surface homeomorphisms Rotation theory is one of the main tools to understand and classify the dynamical behaviour on surfaces. Originated by Henri Poincare in the context of orientationpreserving circle homeomorphisms and flows on the twotorus, it has further been developed for twist maps of the annulus and homeomorphisms of the torus. However, many fundamental questions still remain open, in particular for the case of torus homeomorphisms. 