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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
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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} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3957812}