Chaotic Dynamics of Binary Systems

Abstract

We propose a theory of chaos for discrete systems, based on their representation in a space of ``binary histories'', ${\mathcal{B}}^{\infty }$. We show that ${\mathcal{B}}^{\infty }$ is a metrizable Cantor set which embeds the attractor $\Lambda$, itself also a Cantor set.

TeX file, 23 pages, please contact the authors for figures The first two sections were rewritten to interpret our results (theory of chaos on a space of binary histories) in the context of existing mathematical literature on the dynamics of asymmetric spin glasses and cellular automata