A note on chaotic unimodal maps and applications
Cangtao Zhou, X. T. He, Minjing Yu, Lock Yue Chew, Xingang Wang · Chaos An Interdisciplinary Journal of Nonlinear Science · 2006
Based on the word-lift technique of symbolic dynamics of one-dimensional unimodal maps, we investigate the relation between chaotic kneading sequences and linear maximum-length shift-register sequences. Theoretical and numerical evidence that the set of the maximum-length shift-register sequences is a subset of the set of the universal sequence of one-dimensional chaotic unimodal maps is given. By stabilizing unstable periodic orbits on superstable periodic orbits, we also develop techniques to control the generation of long binary sequences.