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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Bounded remainder sets under torus exchange transformations
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by 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.
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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