Transitivity, mixing and chaos for a class of set-valued mappings  

作　　者：LIAO Gongfu, WANG Lidong & ZHANG Yucheng Institute of Mathematics, Jilin University, Changchun 130012, China Institute of Nonlinear Information Technology, Dalian Nations University, Dalian 116600, China Department of Mathematics, University of Science and Technology of China, Hefei 230026, China 

出　　处：《Science China Mathematics》2006年第1期1-8,共8页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.19971035);the Innovation Foundation of Jilin University(Grant No.2004CZ051).

摘　　要：Consider the continuous map f : x → X and the continuous map f of K,(X) into itself induced by f, where X is a metric space and K(X) the space of all non-empty compact subsets of x endowed with the Hausdorff metric. According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli, we investigate the relations between f and f in the related dynamical properties such as transitivity, weakly mixing and mixing, etc. And by using the obtained results, we give the satisfied answers to Roman-Flores's question and Fedeli's question.Consider the continuous map f: X → X and the continuous map (f-) of K(X)into itself induced by f, where X is a metric space and K(X) the space of all non-empty compact subsets of X endowed with the Hausdorff metric. According to the questions whether the chaoticity of f implies the chaoticity of (f-) posed by Román-Flores and when the chaoticity of f implies the chaoticity of (f-)posed by Fedeli,we investigate the relations between f and (f-) in the related dynamical properties such as transitivity, weakly mixing and mixing etc.And by using the obtained results,we give the satisfied answers to Román-Flores's question and Fedeli's question.

关 键 词：SET-VALUED mapping  transitivity  WEAK mixing  mixing  chaos. 

分 类 号：O189.11[理学—数学]