Professor Peter Kloeden has research interests in dynamical systems and their applications. His PhD thesis (University of Queensland, 1975) provided early contributions to chaos theory. He subsequently made significant contributions to mathematical meteorology, especially concerning well-posedness, existence and uniqueness for the quasi-geostrophic equations, which influenced numerical practice in meteorology.
Since the 1980s, Peter Kloeden played a key role in the development of the theory of random dynamical systems. Motivated by the need to have suitable numerical methods to explore random dynamics, he wrote his seminal book on numerics for stochastic differential equations (Springer 1992) with Eckhard Platen. This book filled a huge gap and established an important research area which substantially influenced both numerics and stochastics. The book is still the main reference for numerics of stochastic differential equations and started a whole industry of new developments and applications, for instance in computational finance, again considerably influenced by Peter Kloeden.
Since the 1990s, Peter Kloeden focused on nonautonomous dynamical systems, both random (i.e. driven by a metric dynamical system) and deterministic (i.e. driven by a flow on a compact space). His results have numerous applications, for instance to synchronised, switching and control systems.
In 2005, Peter was awarded the W.T. and Idalia Reid prize by the Society for Industrial and Applied Mathematics (SIAM) for his fundamental contributions to the theoretical and computational analysis of differential equations, and recently, he has been elected as a Fellow of SIAM.
Research at Imperial College LondonThe main lines of research to be developed during his stay at Imperial College London are
Teaching at Imperial College LondonPeter Kloeden will teach a five-week course on Taylor expansions and numerical approximation of stochastic partial differential equations.