Almost periodicity and distributional chaos in Banach space

Abstract

Let (X,∥·∥) be a Banach space, f : X → X continous Freche't differentiable map.Denote the set of almost periodic point by A(f).In this paper,we prove that there exists an uncountable set Λ such that f |Λ is distributionally chaotic,and Λ ⊂ A(f). © 2009 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering.