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Mat. Sb., 2018, Volume 209, Number 9, Pages 3–18 (Mi msb8936)  

New examples of Besicovitch transitive cylindrical cascades

A. V. Kochergin

Faculty of Economics, Lomonosov Moscow State University

Abstract: New examples of transitive cylindrical cascades with discrete orbits (the Besicovitch property) are constructed. For each $\gamma\in(0,1)$ there exists a cylindrical cascade over a rotation of the circle, with a $\gamma$-Hölder continuous function, that has the Besicovitch property; furthermore, the Hausdorff dimension of the set of points on the circle which have discrete orbits is at least $1-\gamma$. This improves (by $\varepsilon$) an earlier estimate. In addition, an example of a cascade with discrete orbits such that the corresponding function satisfies the Hölder condition with each exponent $\gamma\in(0,1)$ is constructed.
Bibliography: 16 titles.

Keywords: transitive cylindrical cascade, discrete orbit, Hausdorff dimension.

DOI: https://doi.org/10.4213/sm8936

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English version:
Sbornik: Mathematics, 2018, 209:9, 1257–1272

Bibliographic databases:

Document Type: Article
UDC: 517.983
MSC: 37E30
Received: 07.03.2017 and 04.09.2017

Citation: A. V. Kochergin, “New examples of Besicovitch transitive cylindrical cascades”, Mat. Sb., 209:9 (2018), 3–18; Sb. Math., 209:9 (2018), 1257–1272

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