Chaotic Pairs for Shift Maps
Houston Journal of Math
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.
Averbeck, Nathan and Raines, Brian E., "Chaotic Pairs for Shift Maps" (2016). Science and Mathematics Faculty Publications. 361.