Introduction:
The programme `Complexity of geometry and analysis of larger scale Dynamical Systems' considers the larger scale geometry and dynamics in the product of higher dimensional phase space and parameter space. On the one hand we extend the more familiar theory of lower dimensional dynamics, also applying this by center manifolds, etc. What is lower depends a bit on the precise context, but in general the dimensions for flows do not exceed 2 or 3. Here any form of generalisation can be important. On the other hand we also are interested in genuinely in larger scale phenomena, for instance where multiple resonances play a role. Here one may apply Kolmogorov-Arnold-Moser Theory as well as Singularity Theory, often starting off from normal form approximations and the perturbative point of view, but also (numerical) continuations of these can be great importance. Here computational and algorithmic aspects play an important role. The interest is formed by theoretical results as well as by applications, e.g., to population or climate models. In the theoretical approach coupled cell system may play a role. |