Aspekte niedrig-dimensionaler und nicht-autonomer Dynamischer Systeme

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Ergodic Theory and Dynamical Systems have found their applications in basically all sciences and many other fields of mathematics. The aim of this research project is to make substantial contributions to this field, by analysing several types of low-dimensional and/or non-autonomous dynamical systems. A common feature of the systems under consideration is the lack, or irrelevance, of periodic orbits. This renders their investigation particularly difficult, since in the vast majority of situations where the long-term behaviour of a dynamical system is well-understood, the existence of periodic orbits is a crucial feature and often the starting point of any analysis. In contrast to this, periodic point free dynamics are still rather poorly understood in general, such that new concepts and ideas are required for their description. The issues which should be addressed in particular include the role of so-called strange nonchaotic attractors in the classification of quasiperiodically forced circle maps, nonautonomous bifurcation theory with a particular focus on the two-step scenario for the non-autonomous Hopf bifurcation, and the classification of the dynamics of toral homeomorphisms. Applications to physics and biology, which shall be considered likewise, include the description of multi-frequency forced oscillators and neuronal coding under the influence of external noise.