Das, Tushar, Fishman, Lior, Simmons, David orcid.org/0000-0002-9136-6635 et al. (1 more author) (2018) Badly approximable vectors and fractals defined by conformal dynamical systems. Mathematical Research Letters. ISSN 1945-001X
Abstract
We prove that if $J$ is the limit set of an irreducible conformal iterated function system (with either finite or countably infinite alphabet), then the badly approximable vectors form a set of full Hausdorff dimension in $J$. The same is true if $J$ is the radial Julia set of an irreducible meromorphic function (either rational or transcendental). The method of proof is to find subsets of $J$ that support absolutely friendly and Ahlfors regular measures of large dimension. In the appendix to this paper, we answer a question of Broderick, Kleinbock, Reich, Weiss, and the second-named author ('12) by showing that every hyperplane diffuse set supports an absolutely decaying measure.
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Copyright, Publisher and Additional Information: | This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details | ||||
Keywords: | math.NT, math.DS | ||||
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Institution: | The University of York | ||||
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) | ||||
Funding Information: |
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Depositing User: | Pure (York) | ||||
Date Deposited: | 21 Feb 2017 14:00 | ||||
Last Modified: | 06 Dec 2023 11:44 | ||||
Published Version: | https://doi.org/10.4310/MRL.2018.v25.n2.a5 | ||||
Status: | Published online | ||||
Refereed: | Yes | ||||
Identification Number: | https://doi.org/10.4310/MRL.2018.v25.n2.a5 | ||||
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Description: Badly approximable vectors