Mathematical Notes

, Volume 99, Issue 3–4, pp 382–389 | Cite as

Besicovitch cylindrical transformation with a Hölder function

  • A. V. KocherginEmail author


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 − γε.


cylindrical transformation Besicovitch property Hölder property Hausdorff dimension 


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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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