title: β-expansion attractors observed in A/D converters.
abstract: The recently proposed β-encoders, analog-to-digital converters using an amplifier with a factor β and a flaky quantizer with threshold ν, have proven to be explained by the deterministic dynamics of multi-valued Rényi-Parry maps. Such a map is locally eventually onto [ν-1, ν), which is topologically conjugate to Parry's (β,α)-map with α=(β-1)(ν-1). This implies that β-encoders have a closed subinterval [ν-1,ν), which includes an attractor. Thus, the iteration of the multi-valued Rényi-Parry map performs the β-expansion of x while quantization errors in β-encoders behave chaotically and do not converge to a fixed point. This β-expansion attractor is relatively simpler than previously reported attractors. The object of this paper is twofold: to observe the embedded attractors in the β-encoder and to identify attractors that are useful for spread-spectrum codes and optimization techniques using pseudo-random numbers.
authors.affiliation: Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka 819-0395, Japan. kohda@inf.kyushu-u.ac.jp
authors.forename: Tohru
authors.initials: T
authors.lastname: Kohda
authors.forename: Yoshihiko
authors.initials: Y
authors.lastname: Horio
authors.forename: Kazuyuki
authors.initials: K
authors.lastname: Aihara