Topological Entropy,Zero-dimensional Dynamical Models And Universal Real Flows

This thesis studies some dynamical properties in ergodic theory and topological dynam-ics,concerning proximality,asymptoticity,chaos,entropy,topological predictability,embeddability and universality,as well as zero-dimensional models.It consists of six parts.The first part presents some elementary theory of dynamical systems,including basic notions,necessary tools and classical results that will be used in other parts.In the second part,we study the relation between zero topological entropy and topological predictability for actions of countable torsion-free locally nilpotent groups.The third part focuses on mean proximality and mean Li-Yorke chaos,including a new condition that implies mean Li-Yorke chaos and a new characterization of mean proximal systems.In the fourth part,we consider stable sets,mean Li-Yorke chaos and positive topological entropy for actions of countable infinite discrete bi-orderable amenable groups,where several applications are also included.The fifth part is devoted to the study of zero-dimensional isomorphic dynamical models and realizations of assignments on Choquet simplices.The sixth part concentrates on embeddability and universality of real flows,including a satisfactory refinement of the classical Bebutov-Kakutani dynamical em-bedding theorem and an explicit universal flow.