An Ergodic Theory of Binary Operations - Part I: Key Properties

Ergodic Properties of Signed Binary Expansions

Every integer n has a unique signed binary expansions of the form

Topological structure on generalized approximation space related to n-arry relation

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

Ergodic Properties of Signed Binary Expansionskarma Dajani ,

Chaotic Sequences of I.I.D. Binary Random Variables with Their Applications to Communications

The Bernoulli shift is a fundamental theoretic model of a sequence of independent and identically distributed(i.i.d.) binary random variables in probability theory, ergodic theory, information theory, and so on. We give a simple sufficient condition for a class of ergodic maps with some symmetric properties to produce a chaotic sequence of i.i.d. binary random variables. This condition is expre...

Orderings of the rationals and dynamical systems

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of rather standard topics such as SternBrocot and Farey trees and their connections with continued fraction expansion and the question mark function. In the seco...