Besicovitch cascades and bounded partial quotients

• Autores: Andrey Kochergin
• Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 5, Nº. 2, 2020, págs. 267-278
• Idioma: inglés
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• Resumen

  • The article continues a series of works studying cylindrical transformations having discrete orbits (Besicovitch cascades).

    For any γ ∈ (0,1) and any ε > 0 we construct a Besicovitch cascade over some rotation with bounded partial quotients, and with a γ–Hölder function, such that the Hausdorff dimension of the set of points in the circle having discrete orbits is greater than 1−γ −ε.