Study On The Set Of Chain Recurrent Points On The Tent-like Mapping

The complexity of continuous mapping on compact metric space has always been the focus of topological dynamical systems research.This paper focuses on the chain recurrent point set and strong chain recurrent point set of tent-like mappingIn the first chapter,the origin and development of the topolo-gy dy namic system in detail,and the preliminary progress that has been made are introducedIn the second chapter,the basic knowledge of topology,the ba-sic def,inition theorem,and the basic knowledge of the topology dy-namic system are introducedIn chapter 3,the right high tent-like mapping is defined.The properties of right high tent-like mapping chain recurrent point set and strong chain recurrent point set are discussed.The conclusions are as follows(1)0<λ<t,SCR(ft,λ)=CR(ft,λ)={0}∪[λ,1](2)λ=t,SCR(ft,λ)=CR(ft,λ)={0}∪[t,1](3)t<λ≤1,SCR(ft,λ)=CR(ft,λ)={0,at,λ}In chapter 4,the left high tent-like mapping is defined.The prop-erties of left high tent-like mapping chain recurrent point set is discussed.The conclusions are as follows(1)0<t<1/2,0<λ≤t,CR(gt,λ)=[0,1](2)1/2+t≤λ≤t2-t+1,CR(h1,t,λ)={1/2-t}λ[λ,1](3)t2-t+1<λ≤1,CR(h1,t,λ)=Fix(h1,t,λ)={1/2-t,1-λ-λt2+λt/1-λ-t2+t2}...