For closed hyperbolic dynamical systems Pesin's theorem identifies the Kolmogorov-Sinai (KS) entropy with the sum of positive Lyapunov exponents. An extension of this equation to open systems is provided by the escape rate formula, which yields the rate of exponential escape of particles in terms of the difference between positive Lyapunov exponents and the KS entropy on a fractal repeller. This rate can, in turn, be related to the diffusion coefficient of a dynamical system thus providing a fundamental formula expressing a physical quantity in terms of dynamical systems characteristics.

In my talk I will outline these facts step by step thus motivating the main question of my talk: Can this concept be carried over to an intermittent map exhibiting anomalous diffusion, i.e., where the mean square displacement grows nonlinearly in time? First attempts for solving this problem involve studying `aging' phenomena caused by infinite invariant measures - and pose a lot of further open questions.