Distributional Chaos In A Sequence

Content: The system induced by the continuous self-map of the compact metric space is called the dynamic system or the compact system. In this paper we mainly discuss the distributively chaotic properties in a sequence of the dynamic system, and as an application, we will discuss the chaotic properties of a model of an exchange economy. The main results be showed as following:(1) The continuous map of a compact metric space is distributively chaotic (i.e. distributively chaotic in sequence of natural numbers) if and only if its each iterate is distributively chaotic.(2) We prove a sufficient condition for the continuous map of a compact metric space for being distributively chaotic in a sequence, and by this result we proved that a continuous map of an interval is Li-Yorke chaotic if and only if it is distributively chaotic in a sequence.(3) In order to discuss the problem about the chaotic properties of the differentiable operator dynamical system, we prove the distributively chaotic properties in a sequence of the differentiable operator dynamical system by means of constructing .(4) Discuss the chaotic properties of a model involving two individuals and two goods of an exchange economy.