Chaos on the Multi-Dimensional Cube

Abstract

In this article, we show that a chaotic behavior can be found on a cube with arbitrary finite dimension. That is, the cube is a quasi-minimal set with Poincare chaos. Moreover, the dynamics is shown to be Devaney and Li-Yorke chaotic. It can be characterized as a domain-structured chaos for an associated map. Previously, this was known only for unit section and for Devaney and Li-Yorke chaos.