Measurements in Dynamical Systems / Carlangelo Liverani (U Roma "Tor Vergata")
theorem classifies all the possible outcomes in terms of the invariant measures of the system. The study of the, much more realistic, finite time averages is equivalent to investigating at which speed the [...] knowledge shows that the behaviour depends drastically from the properties of the system. In the study of such a problem functional analysis, probability theory, and geometry play major roles. I will attempt