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A class of primitive substitutions and scrambled sets

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Science China Mathematics 2008年第3期51卷 369-375页

作者： liao gongfu FAN QinJie WANG LiDong College of Mathematics Jilin Normal UniversitySiping 136000China College of Mathematics Jilin UniversityChangchun 130012China Department of Mathematics Dalian Nationalities UniversityDalian 116600China

Consider the subshifts induced by constant-length primitive substitutions on two symbols. By investigating the equivalent version for the existence of Li-Yorke scrambled sets and by proving the non-existence of Schweizer-Smítal scrambled sets, we completely reveal for this class of subshifts the chaotic behaviors possibly occurring in the sense of Li-Yorke and Schweizer-Smítal.

关键词： primitive substitution subshift Li-Yorke scrambled set Schweizer-Smítal scrambled set 54H20 58F03 58F08

CHAOS FOR MIXING TRANSFORMATIONS

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Chinese Annals of Mathematics,Series B 1994年第4期15卷 501-506页

作者： liao gongfu (Department of Mathematics,Jilin University, Changchun 130023, China.) JILIN UNIV DEPT MATH CHANGCHUN 130023 PEOPLES R CHINA

For a class of mixing transformations of a compact metric space it is proved that each chaoticsubset is'small' but the possibility for any finite subset to display chaotic behavior is 'large'.

关键词： Compact metric space Chaotic subset Mixing transformation Topological mixing map.

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

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Science China Mathematics 2006年第1期49卷 1-8页

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 Institute of Mathematics Jilin University Changchun China Institute of Nonlinear Information Technology Dalian Nations University Dalian China Department of Mathematics University of Science and Technology of China Hefei China

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.

关键词： set-valued mapping, transitivity, weak mixing, mixing, chaos.