|
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.
Citation:
Alexey Klimenko, “Spatial limit theorem for interval exchange transformations”, Mosc. Math. J., 19:2 (2019), 343–356
Linking options:
https://www.mathnet.ru/eng/mmj738 https://www.mathnet.ru/eng/mmj/v19/i2/p343
|
Statistics & downloads: |
Abstract page: | 224 | References: | 52 |
|