Abstract
We prove that almost every finite collection of matrices in GLd (ℝ) and SLd({ℝ) with positive entries is Diophantine. Next we restrict ourselves to the case d=2. A finite set of SL2(ℝ) matrices induces a (generalized) iterated function system on the projective line ℝℙ1. Assuming uniform hyperbolicity and the Diophantine property, we show that the dimension of the attractor equals the minimum of 1 and the critical exponent.
Original language | English |
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Pages (from-to) | 12639-12669 |
Number of pages | 31 |
Journal | International Mathematics Research Notices |
Volume | 2021 |
Issue number | 16 |
DOIs | |
State | Published - 1 Aug 2021 |
Bibliographical note
Publisher Copyright:© 2020 The Author(s).
Funding
Both authors were supported by the Israel Science Foundation grant 396/15 (PI. B.\Solomyak).
Funders | Funder number |
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Israel Science Foundation | 396/15 |