Furstenberg family and chaos

作     者：Jin-cheng XIONG Jie LU Feng TAN 

作者机构：School of Mathematical SciencesSouth China Normal UniversityGuangzhou 510631China 

出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))

年 卷 期：2007年第50卷第9期

页      面：1325-1333页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.10471049) 

主　　题：Furstenberg family scrambled pair scrambled set generically F-chaotic map generically strongly chaotic map 

摘      要：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∈*** 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 *** the present paper we explore the basic properties of the set of F-scrambled pairs of a *** generically F-chaotic system and the generically strongly F-chaotic system are defined.A criterion for a generically strongly F-chaotic system is showed.