Linear Li–Yorke Chaos in a Finite-Dimensional Space with Weak Topology

Abstract

It is well known that a finite-dimensional linear system cannot be chaotic. In this article, by introducing a weak topology into a two-dimensional Euclidean space, it shows that Li–Yorke chaos can be generated by a linear map, where the weak topology is induced by a linear functional. Some examples of linear systems are presented, some are chaotic while some others regular. Consequently, several open problems are posted.