Article
Besicovitch cascades and bounded partial quotients
Authors
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.
Keywords
Besicovitch, cylinder transformation, Hausdorff dimension, Hölder function, discrete orbit, partial quotients, 37B05, 37C45
Citation
Kochergin, A. (2020). Besicovitch cascades and bounded partial quotients. Applied Mathematics and Nonlinear Sciences, 5(2), 267–278. https://doi.org/10.2478/amns.2020.2.00050
A. Kochergin, “Besicovitch cascades and bounded partial quotients,” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, pp. 267–278, 2020, doi: 10.2478/amns.2020.2.00050.
Kochergin A. Besicovitch cascades and bounded partial quotients. Applied Mathematics and Nonlinear Sciences. 2020;5(2):267–278. doi:10.2478/amns.2020.2.00050.
Kochergin, A. (2020), ‘Besicovitch cascades and bounded partial quotients’, Applied Mathematics and Nonlinear Sciences, 5(2), pp. 267–278. Available at: https://doi.org/10.2478/amns.2020.2.00050.
Kochergin, Andrey. “Besicovitch Cascades and Bounded Partial Quotients.” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, 2020, pp. 267–278. https://doi.org/10.2478/amns.2020.2.00050.
Kochergin, Andrey. “Besicovitch Cascades and Bounded Partial Quotients.” Applied Mathematics and Nonlinear Sciences 5, no. 2 (2020): 267–278. https://doi.org/10.2478/amns.2020.2.00050.
Export citation
Published by: Engineering Journals
