On finite time theory for nonautonomous dynamical systems and some open problems

This talk presents a survey on recent developments of finite theory for nonautonomous dynamical systems. The theory is useful for studying coherent structures in transport and mixing of passive and active scalars in fluids. Several diagnostic quantities have been proposed to visualize these structures, either from the geometric views such as finite time Lyapunov exponents or from probabilistic views such as finite time entropy. Further work is necessary to explore the relation between those methods.

(The talk is based on the joint work with Stefan Siegmund.)