Background. The last two decades have seen a steadily increasing interest in the development of set-oriented numerical methods for the analysis of dynamical systems and applications. Of particular interest is the approximation of certain invariant sets: these are subsets of the state space that are invariant under the evolution of the dynamical system. Higher-dimensional objects such as chaotic attractors or invariant manifolds of hyperbolic sets are especially important, because knowledge of these objects is crucial for the understanding of the global system behaviour. In addition, other important quantities associated with these invariant sets have been examined, such as Lyapunov exponents or invariant measures. Set-oriented methods thus complement the classical approaches to the analysis of dynamical systems, which typically only consider the local behaviour of the dynamics.
Set-oriented methods are applicable to many different classes of problems, for example, to solve global optimisation problems, multi-objective optimisation problems, and optimal control problems. In addition, methods to determine metastable, almost-invariant or nearly-cyclic states in dynamical systems have been developed in recent years, as well as to investigate the associated transport processes between relevant areas in the state. These analyses are based on an approximation of the underlying dynamics through Markov models, which in particular also makes viewing high-dimensional systems possible. Appropriate extensions to nonautonomous, time-dependent or stochastically driven dynamical systems are the subject of current research.
The goal of this workshop is to bring high-profile international scientists from mathematics, physics and fluid mechanics together to discuss the latest developments in the field of set-oriented numerics, as well as to promote possible applications. The workshop considers theoretical foundations of set-oriented numerical methods and practical aspects. This meeting will allow constructive discussions about the advantages and disadvantages of different approaches, and will facilitate the development of innovative ways to combine and improve the current state-of-the-art, as well as opening up new application fields.Key topics. The themes for this workshop will be primarily concerned with the following topics: