Article ID Journal Published Year Pages File Type
4595290 Journal of Number Theory 2008 11 Pages PDF
Abstract

In this paper, we obtain strong density results for the orbits of real numbers under the action of the semigroup generated by the affine transformations T0(x)=x/a and T1(x)=bx+1, where a,b>1. These density results are formulated as generalizations of the Dirichlet approximation theorem and improve the results of Bergelson, Misiurewicz, and Senti. We show that for any x,u>0 there are infinitely many elements γ in the semigroup generated by T0 and T1 such that |γ(x)−u|

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory