Bounded remainder sets under torus exchange transformations
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V. G. Zhuravlev
Translated by: A. Luzgarev - St. Petersburg Math. J. 27 (2016), 245-271
- DOI: https://doi.org/10.1090/spmj/1386
- 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.References
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Bibliographic Information
- V. G. Zhuravlev
- Affiliation: Vladimir State University, pr. Stroiteley 11, 600024 Vladimir, Russia
- Email: vzhuravlev@mail.ru
- Received by editor(s): September 1, 2014
- Published electronically: January 29, 2016
- Additional Notes: Supported by RFBR (grant no. 14-01-00360)
- © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 27 (2016), 245-271
- MSC (2010): Primary 05B45; Secondary 51M20
- DOI: https://doi.org/10.1090/spmj/1386
- MathSciNet review: 3444463