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The Topological Sensitivity with respect to Furstenberg Families
Discrete Dynamics in Nature and Society ( IF 1.4 ) Pub Date : 2020-06-04 , DOI: 10.1155/2020/7684072 Tengfei Wang 1 , Kai Jing 1 , Jiandong Yin 1
Discrete Dynamics in Nature and Society ( IF 1.4 ) Pub Date : 2020-06-04 , DOI: 10.1155/2020/7684072 Tengfei Wang 1 , Kai Jing 1 , Jiandong Yin 1
Affiliation
In this work, a dynamical system means that is a topological space and is a continuous map. The aim of the article is to introduce the conceptions of topological sensitivity with respect to Furstenberg families, -topological sensitivity, and multisensitivity and present some of their basic features and sufficient conditions for a dynamical system to possess some sensitivities. Actually, it is proved that every topologically ergodic but nonminimal system is syndetically sensitive and a weakly mixing system is -thickly topologically sensitive and multisensitive under the assumption that admits some separability.
中文翻译:
关于Furstenberg家庭的拓扑敏感性
在这项工作中,动力系统 表示这是一个拓扑空间,是连续的地图。本文的目的是介绍有关Furstenberg族的拓扑敏感性的概念-拓扑敏感性和多重敏感性,并介绍它们的一些基本特征和动力学系统具有某些敏感性的充分条件。实际上,事实证明,在允许某些可分离性的假设下,每个拓扑遍历但非最小的系统都是联合敏感的,而弱混合系统是-稠密的拓扑敏感和多敏感的。
更新日期:2020-06-04
中文翻译:
关于Furstenberg家庭的拓扑敏感性
在这项工作中,动力系统 表示这是一个拓扑空间,是连续的地图。本文的目的是介绍有关Furstenberg族的拓扑敏感性的概念-拓扑敏感性和多重敏感性,并介绍它们的一些基本特征和动力学系统具有某些敏感性的充分条件。实际上,事实证明,在允许某些可分离性的假设下,每个拓扑遍历但非最小的系统都是联合敏感的,而弱混合系统是-稠密的拓扑敏感和多敏感的。