title: A note on chaotic unimodal maps and applications.
abstract: 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.
authors.affiliation: Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, People's Republic of China.
authors.forename: C T
authors.initials: CT
authors.lastname: Zhou
authors.forename: X T
authors.initials: XT
authors.lastname: He
authors.forename: M Y
authors.initials: MY
authors.lastname: Yu
authors.forename: L Y
authors.initials: LY
authors.lastname: Chew
authors.forename: X G
authors.initials: XG
authors.lastname: Wang
mesh_terms: 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