<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The article continues a series of works studying cylindrical transformations having discrete orbits (Besicovitch cascades). For any <italic>γ</italic> ∈ (0,1) and any <italic>ɛ</italic> > 0 we construct a Besicovitch cascade over some rotation with bounded partial quotients, and with a <italic>γ</italic>–Hölder function, such that the Hausdorff dimension of the set of points in the circle having discrete orbits is greater than 1 − <italic>γ</italic>− <italic>ɛ</italic>.</p></abstract>

The article continues a series of works studying cylindrical transformations having discrete orbits (Besicovitch cascades). For any γ ∈ (0,1) and any ɛ > 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− ɛ.

Besicovitch cascades and bounded partial quotients

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Besicovitch cascades and bounded partial quotients"}

The article continues a series of works studying cylindrical transformations having discrete orbits (Besicovitch cascades). For any γ ∈ (0,1) and any ɛ > 0 we...

Besicovitch cascades and bounded partial quotients

Published Online: Nov 16, 2020

Page range: 267 - 278

Received: Jan 23, 2020

Accepted: Apr 04, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00050

Keywords
Besicovitch, cylinder transformation, Hausdorff dimension, Hölder function, discrete orbit, partial quotients

© 2020 Andrey Kochergin, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Besicovitch cascades and bounded partial quotients

Published Online: Nov 16, 2020

Page range: 267 - 278

Received: Jan 23, 2020

Accepted: Apr 04, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00050

KeywordsBesicovitch, cylinder transformation, Hausdorff dimension, Hölder function, discrete orbit, partial quotients

© 2020 Andrey Kochergin, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Keywords
Besicovitch, cylinder transformation, Hausdorff dimension, Hölder function, discrete orbit, partial quotients