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.
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Original Russian Text © A. V. Kochergin, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 3, pp. 366–375.
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Kochergin, A.V. Besicovitch cylindrical transformation with a Hölder function. Math Notes 99, 382–389 (2016). https://doi.org/10.1134/S0001434616030068
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DOI: https://doi.org/10.1134/S0001434616030068