Resumen de Besicovitch cascades and bounded partial quotients

Andrey Kochergin

• 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.