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
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.