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Mat. Zametki, 2016, Volume 99, Issue 3, Pages 366–375 (Mi mz10875)  

This article is cited in 2 scientific papers (total in 2 papers)

Besicovitch Cylindrical Transformation with a Hölder Function

A. V. Kochergin

Lomonosov Moscow State University

Abstract: For any $\gamma\in(0,1)$ and $\varepsilon>0$, we construct a cylindrical cascade with a $\gamma$-Hölder function over some rotation of the circle. This transformation has the Besicovitch property; i.e., it is topologically transitive and has discrete orbits. The Hausdorff dimension of the set of points of the circle that have discrete orbits is greater than $1-\gamma-\varepsilon$.

Keywords: cylindrical transformation, Besicovitch property, Hölder property, Hausdorff dimension.

DOI: https://doi.org/10.4213/mzm10875

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English version:
Mathematical Notes, 2016, 99:3, 382–389

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 17.05.2015

Citation: A. V. Kochergin, “Besicovitch Cylindrical Transformation with a Hölder Function”, Mat. Zametki, 99:3 (2016), 366–375; Math. Notes, 99:3 (2016), 382–389

Citation in format AMSBIB
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\by A.~V.~Kochergin
\paper Besicovitch Cylindrical Transformation with a~H\"older Function
\jour Mat. Zametki
\yr 2016
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\pages 366--375
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\pages 382--389
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. S. Efremova, “Dynamics of skew products of interval maps”, Russian Math. Surveys, 72:1 (2017), 101–178  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. V. Kochergin, “New examples of Besicovitch transitive cylindrical cascades”, Sb. Math., 209:9 (2018), 1257–1272  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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