International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 143-146
doi:10.1155/S0161171294000190

Dynamics of the radix expansion map

Ben Goertzel, Harold Bowman, and Richard Baker

Department of Mathematics, University of Nevada, Las Vegas, Las Vegas 89154, NV, USA

Received 13 April 1992; Revised 14 April 1993

Copyright © 1994 Ben Goertzel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The chaotic dynamics of the map ϕ(x)=(βx+α)(mod1) are studied using Parry's β-expansion. It is shown that for 1<β<2, a≥0, the number of periodic points of period n is 0(βn).