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Matematicheskie Zametki, 2016, Volume 99, Issue 3, Pages 366–375
DOI: https://doi.org/10.4213/mzm10875 (Mi mzm10875) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Besicovitch Cylindrical Transformation with a Hölder Function

A. V. Kochergin

Lomonosov Moscow State University
Full-text PDF (516 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm10875
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.
Received: 17.05.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 3, Pages 382–389
DOI: https://doi.org/10.1134/S0001434616030068
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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