Researches On Chaos Of Topological Dynamical Systems

This dissertation mainly studies the properties of distributively chaotic sets of the one-sided symbolic dynamic systems and the related properties of the large deviations theorem of non-autonomous discrete dynamic systems and so on.This dissertation is divided into four chapters,the specific contents are as follows:Chapter 1 mainly introduces the historical backgrounds and current research situation of the related problems considered in this dissertation as well as some preliminary knowledge required for this dissertation.Chapter 2 mainly studies the existence of distributively chaotic sets in the sets of irregularly recurrent points and proper positive upper Banach density recurrent points of the one-sided symbolic systems and obtains the follows results:there exists uncountable distributively chaotic sets in the sets of irregularly recurrent point and proper positive upper Banach density recurrent points of the one-sided symbolic systems.Chapter 3 firstly introduces the large deviations theorem in non-autonomous discrete dynamic systems,then studies some dynamic properties of non-autonomous discrete dynamic systems with the large deviations theorem and obtains:let(X,F)be a non-autonomous system and,u be a Borel measure on X with a full support and if(X,F,?)satisfies the large deviations theorem and F is topologically strongly ergodic,then F is ergodically sensitive;if(X,F,?)satisfies the large deviations theorem in a sequence of positive integers,then F is topologically ergodic;if(X,F,?)satisfies the large deviations theorem and each measurable set with positive measure with respect to ? has a nonempty interior and F is topologically strongly ergodic,then ? is expansive.Chapter 4 is the summary and prospect of this dissertation.In this chapter,we put forward some questions to be researched in future.