Diophantine Property of Matrices and Attractors of Projective Iterated Function Systems in ℝℙ1

Boris Solomyak, Yuki Takahashi

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)12639-12669
Number of pages31
JournalInternational Mathematics Research Notices
Volume2021
Issue number16
DOIs
StatePublished - 1 Aug 2021

Bibliographical note

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© 2020 The Author(s).

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