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Mosc. Math. J., 2019, Volume 19, Number 2, Pages 343–356 (Mi mmj738)  

Spatial limit theorem for interval exchange transformations

Alexey Klimenkoab

a Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, 119991, Moscow, Russia
b National Research University Higher School of Economics, Usacheva str. 6, 119048, Moscow, Russia

Abstract: We prove a spatial limit theorem for generic interval exchange transformations (IETs): for a generic IET the normalized ergodic sums of a Lipschitz function have the same asymptotic behavior of distributions as the behaviour of the distributions of the ergodic integrals for a generic translation flow on a flat surface, which was described by A. Bufetov.

Key words and phrases: limit theorem, interval exchanger transformation, Bufetov cocycles, finitely additive measures.

DOI: https://doi.org/10.17323/1609-4514-2019-19-2-343-356

Full text: http://www.mathjournals.org/.../2019-019-002-007.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 37E05; Secondary 60F05

Citation: Alexey Klimenko, “Spatial limit theorem for interval exchange transformations”, Mosc. Math. J., 19:2 (2019), 343–356

Citation in format AMSBIB
\Bibitem{Kli19}
\by Alexey~Klimenko
\paper Spatial limit theorem for interval exchange transformations
\jour Mosc. Math.~J.
\yr 2019
\vol 19
\issue 2
\pages 343--356
\mathnet{http://mi.mathnet.ru/mmj738}
\crossref{https://doi.org/10.17323/1609-4514-2019-19-2-343-356}


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