Abstract:
While hyperbolic dynamical systems obey the Sinai Central Limit
Theorem, parabolic systems do not: limit distributions have compact
support, exist only along subsequences of times and essentially depend
on the subsequence: for instance, for translation flows, the delta mass
at zero typically arises as a limit distribution along a subsequence.
The survey talk, aimed at undergraduate students,
will aim to give a gentle introduction to limit theorems for parabolic
dynamical systems. The main step is a construction of a special family
of finitely-additive measures on the arcs of trajectories of our flows.
Specific examples include translation flows, horocycle flows (joint work with Giovanni Forni) and tiling flows
(joint work with Boris Solomyak).