Email this article Besicovitch cylindrical transformation with a Hölder function
- Authors: Kochergin A.V.1
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Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 99, No 3-4 (2016)
- Pages: 382-389
- Section: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/149208
- DOI: https://doi.org/10.1134/S0001434616030068
- ID: 149208
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Abstract
For any γ ∈ (0, 1) and ε > 0, we construct a cylindrical cascade with a γ-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 − γ − ε.
About the authors
A. V. Kochergin
Lomonosov Moscow State University
Author for correspondence.
Email: avk@econ.msu.ru
Russian Federation, Moscow
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