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Bounded remainder sets under torus exchange transformations

Author: V. G. Zhuravlev
Translated by: A. Luzgarev
Original publication: Algebra i Analiz, tom 27 (2015), nomer 2.
Journal: St. Petersburg Math. J. 27 (2016), 245-271
MSC (2010): Primary 05B45; Secondary 51M20
Published electronically: January 29, 2016
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Abstract: The object of study is a certain class $ \mathbb{S}$ of exchange transformations of the two-dimensional torus $ \mathbb{T}^2$, obtained by perturbing direct products of two one-dimensional interval exchange transformations. An explicit construction of bounded remainder sets under transformations in $ \mathbb{S}$ is given. Sharp bounds for the deviation functions of such sets are proved and their mean values are calculated.

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Additional Information

V. G. Zhuravlev
Affiliation: Vladimir State University, pr. Stroiteley 11, 600024 Vladimir, Russia

Keywords: Torus exchange transformations, bounded remainder sets on the torus, multidimensional Hecke theorem
Received by editor(s): September 1, 2014
Published electronically: January 29, 2016
Additional Notes: Supported by RFBR (grant no. 14-01-00360)
Article copyright: © Copyright 2016 American Mathematical Society