STATISTICAL DEPENDENCY IN CHAOS

摘要

This paper is concerned with the statistical dependency effects in chaotic map processes, both before and after their discretization at branch boundaries. The resulting processes are no longer chaotic but are left with realizable statistical behavior. Such processes have appeared over several years in the electronic engineering literature. Informal but extended mathematical theory that facilitates the practical calculation of autocorrelation of such statistical behavior, is developed. Both the continuous and discretized cases are treated further by using Kohda's notions of equidistribution and constant-sum to maps which are not onto. Some particularly structured chaotic map processes, and also well-known maps are examined for their statistical dependency, with the tailed shift map family from chaotic communications receiving detailed attention. Several parts of the paper form a brief review of existing theory.