For each sequence of positive real numbers,tending to positive infinity,a Furstenberg family is defined.All these Furstenberg families are compatible with dynamical systems.Then,chaos with respect to such Furstenberg ...For each sequence of positive real numbers,tending to positive infinity,a Furstenberg family is defined.All these Furstenberg families are compatible with dynamical systems.Then,chaos with respect to such Furstenberg families are intently discussed.This greatly improves some classica results of distributional chaos.To confirm the effectiveness of these improvements,the relevant examples are provided finally.展开更多
A dynamical system is called a null system, if the topological sequence entropy along any strictly increasing sequence of non-negative integers is 0. Let 0≦p≦q≦1. A dynamical system is Dqp chaotic, if there is an u...A dynamical system is called a null system, if the topological sequence entropy along any strictly increasing sequence of non-negative integers is 0. Let 0≦p≦q≦1. A dynamical system is Dqp chaotic, if there is an uncountable subset in which any two different points have trajectory approaching time set with lower density p and upper density q. In this paper, we show that there is a null system which is also D3/41/4 chaotic.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11071084 and 11026095)Natural Science Foundation of Guangdong Province(Grant No.10451063101006332)+1 种基金the Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(Grant No.2012LYM 0133)Scientific Technology Planning of Guangzhou Education Bureau(Grant No.2012A075)
文摘For each sequence of positive real numbers,tending to positive infinity,a Furstenberg family is defined.All these Furstenberg families are compatible with dynamical systems.Then,chaos with respect to such Furstenberg families are intently discussed.This greatly improves some classica results of distributional chaos.To confirm the effectiveness of these improvements,the relevant examples are provided finally.
基金supported by National Natural Science Foundation of China (Grant No.11071084)Natural Science Foundation of Guangdong Province (Grant No. 10451063101006332)
文摘A dynamical system is called a null system, if the topological sequence entropy along any strictly increasing sequence of non-negative integers is 0. Let 0≦p≦q≦1. A dynamical system is Dqp chaotic, if there is an uncountable subset in which any two different points have trajectory approaching time set with lower density p and upper density q. In this paper, we show that there is a null system which is also D3/41/4 chaotic.
