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A class of primitive substitutions and scrambled sets 被引量:7
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作者 LIAO GongFu FAN QinJie WANG LiDong 《Science China Mathematics》 SCIE 2008年第3期369-375,共7页
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 Schwei... 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. 展开更多
关键词 primitive substitution SUBSHIFT Li-Yorke scrambled set Schweizer-Smítal scrambled set 54H20 58F03 58F08
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Furstenberg family and chaos 被引量:14
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作者 Jin-cheng XIONG Jie LU Feng TAN 《Science China Mathematics》 SCIE 2007年第9期1325-1333,共9页
A Furstenberg family F is a family,consisting of some subsets of the set of positive integers,which is hereditary upwards,i.e.A?B and A∈F imply B∈F.For a given system(i.e.,a pair of a complete metric space and a con... A Furstenberg family F is a family,consisting of some subsets of the set of positive integers,which is hereditary upwards,i.e.A?B and A∈F imply B∈F.For a given system(i.e.,a pair of a complete metric space and a continuous self-map of the space)and for a Furstenberg family F,the definition of F-scrambled pairs of points in the space has been given,which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be F-scrambled pairs corresponding respectively to suitable Furstenberg family F.In the present paper we explore the basic properties of the set of F-scrambled pairs of a system.The generically F-chaotic system and the generically strongly F-chaotic system are defined.A criterion for a generically strongly F-chaotic system is showed. 展开更多
关键词 Furstenberg family scrambled pair scrambled set generically F-chaotic map generically strongly chaotic map
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Relativization of dynamical properties
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作者 ZHANG GuoHua 《Science China Mathematics》 SCIE 2012年第5期913-936,共24页
In the past twenty years,great achievements have been made by many researchers in the studies of chaotic behavior and local entropy theory of dynamical systems.Most of the results have been generalized to the relative... In the past twenty years,great achievements have been made by many researchers in the studies of chaotic behavior and local entropy theory of dynamical systems.Most of the results have been generalized to the relative case in the sense of a given factor map.In this survey we offer an overview of these developments. 展开更多
关键词 relative entropy asymptotic pair scrambled set local variational principles relative entropy tuple relative topological Pinsker factor relative UPE relative CPE
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CHAOS AND TOPOLOGICAL MIXING OF TREE MAPS
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作者 罗智明 张可村 《Annals of Differential Equations》 2003年第2期160-169,共10页
In the present paper we show that a tree map is totally transitive iff it is topologically mixing. Using this result, we prove that the tree maps having a chaotic (or scrambled) subset with full Lebesgue measure is de... In the present paper we show that a tree map is totally transitive iff it is topologically mixing. Using this result, we prove that the tree maps having a chaotic (or scrambled) subset with full Lebesgue measure is dense in the space consisting of all topologically mixing (transitive, respectively) maps. 展开更多
关键词 topological transitive topological mixing CHAOS scrambled sub set
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