A note on inhomogeneous Diophantine approximation in beta-dynamical system

Authors

  • Y. Ge
  • F. Lü

Keywords:

Beta-dynamical system, beta-expansion, inhomogeneous Diophantine approximation, Lebesgue measure, Hausdorff dimension

Abstract

We study the distribution of the orbits of real numbers under the beta-transformation Tβ for any β>1. More precisely, for any real number β>1 and positive function φ:N→R+, we determine the Lebesgue measure and the Hausdorff dimension of the following set E(Tβ,φ)={(x,y)∈[0,1]×[0,1]:|Tnβx−y|<φ(n) for infinitely many n∈N}. DOI: 10.1017/S0004972714000677

Published

2014-11-13

Issue

Vol. 91 No. 1 (2015)

Section

Articles
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