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Restricted slowly growing digits for infinite iterated function systems

journal contribution
posted on 2025-04-03, 02:28 authored by Gerardo RobertGerardo Robert, Mumtaz HussainMumtaz Hussain, Nikita ShulgaNikita Shulga, Hiroki Takahasi

We prove that the Hausdorff dimension stays the same no matter how slowly the function φ grows. One of the consequences of our result is the recent work of Takahasi (2023), which only dealt with regular continued fraction expansions. We further extend our result to slowly growing products of (not necessarily consecutive) digits.

Funding

GGR, MH, and NS were supported by The Australian Research Council discovery project grant number 200100994. HT was supported by the JSPS KAKENHI 19K21835, 20H01811.

History

Publication Date

2025-09-01

Journal

Journal of Mathematical Analysis and Applications

Volume

549

Issue

1

Article Number

129478

Pagination

15p.

Publisher

Elsevier

ISSN

0022-247X

Rights Statement

© 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

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