A note on chaotic unimodal maps and applications.
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.
Zhou
C T
CT
Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, People's Republic of China.
He
X T
XT
Yu
M Y
MY
Chew
L Y
LY
Wang
X G
XG
D000465:Algorithms; D003198:Computer Simulation; D019277:Entropy; D008433:Mathematics; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D010825:Physics / Q000379:methods*; D013598:Systems Theory