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June 6, 2017 14:00–15:00, Workshop «Moduli Spaces in Moscow: Dynamics and Geometry», Moscow, June 5-9, 2017  


Limit theorems for parabolic systems

A. I. Bufetov
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MP4 437.1 Mb
MP4 1,760.0 Mb
MP4 906.5 Mb

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A. I. Bufetov



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).

Language: English
 
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