Chaos On The Compect System

The system induced by the continuous self-map of the compact metric space is called tdynamic system or the compact system, topological mixing and weakly mixing are importo to investigate asymptotic behavior and topological structure of the orbits of points, If adynamical system is topological mixing or weakly mixing, it must have many chaotic properties under many kinds of meanings. In this paper we mainly discuss the chaotic properties on the general compact space and symbolic space, then reach some important results as follows:Let X be a separable metric space at least two points,and f : X→X be continuouthis paper,we consider dynamical systems on X , and proved that weakly mixing impliesdistributional chaos in a sequence.Let ( X ,f) and (Y ,g) be topological dynamical system, f and g be semi-conjuwe discuss the chaotic properties about it. As an application, we prove that f has a posittopological entropy if and only if it has an uncountably chaotic set in which each point is almost periodic.