Moscow Mathematical Journal

Volume 19, Issue 2, April–June 2019 pp. 343–356.

Spatial Limit Theorem for Interval Exchange Transformations

Authors: Alexey Klimenko (1)
Author institution:(1) Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, 119991, Moscow, Russia; and
National Research University Higher School of Economics, Usacheva str. 6, 119048, Moscow, Russia

Summary:

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.

2010 Math. Subj. Class. Primary: 37E05; Secondary: 60F05

Keywords: Limit theorem, interval exchanger transformation, Bufetov cocycles, finitely additive measures.

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