Science and Mathematics Faculty Publications

Title

Chaotic Pairs for Shift Maps

Document Type

Article

Publication Date

2016

Journal Title

Houston Journal of Math

Volume

42

Issue

4

First Page

1367

Last Page

1372

Abstract

In this short, simple paper we answer a question of Fu and You by considering the properties of chaotic pairs of points in the sense of Li and Yorke for shift maps on symbolic dynamical systems. We show that a pair of points (x, y), in a symbolic dynamical system is chaotic if, and only if, it has a thick set of agreements and infinitely many disagreements. We show that the Banach density of the pairs set of agreements does not indicate whether the pair is chaotic or not, unless that density is exactly one.

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