Statistical independence of generalized chaotic sequences

摘要

We show that any string x(s), x(s+1),... x(s+r). (for any r) constitutes a set of statistically independent random variables given the generalized chaotic sequence x(n) cos[2 pi theta z ''], where z is a typical real number. This result can be generalized to sequences of type x(n) P(z ''), where P(t) is a periodic function. We will discuss the relevance of this result to dynamical systems, real physical experiments, and new technological devices used in secure communications.