<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

Pubblicato online: 16 nov 2020

Pagine: 267 - 278

Ricevuto: 23 gen 2020

Accettato: 04 apr 2020

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

Parole chiave
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.

Besicovitch cascades and bounded partial quotients

Pubblicato online: 16 nov 2020

Pagine: 267 - 278

Ricevuto: 23 gen 2020

Accettato: 04 apr 2020

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

Parole chiaveBesicovitch, 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.

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