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
基金This work was supported by the National Natural Science Foundation of China(Grant No.10471049)
文摘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.
