When is a dynamical system mean sensitive?
Garcia-Ramos, Felipe1,2; Li, Jie3,4; Zhang, Ruifeng5
AbstractThis article is devoted to studying which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things, we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive. On the other hand, we provide an example of a transitive system which is cofinitely sensitive or Devaney chaotic with positive entropy but fails to be mean sensitive. As applications of our theory and examples, we negatively answer an open question regarding equicontinuity/sensitivity dichotomies raised by Tu, we introduce and present results of locally mean equicontinuous systems and we show that mean sensitivity of the induced hyperspace does not imply that of the phase space.
Funding ProjectNSERC ; IMPA ; CAPES ; NNSF of China[11701231] ; NNSF of China[11371339] ; NNSF of China[11571335] ; NNSF of China[11171320] ; NNSF of China[11671094] ; NSF of Jiangsu Province[BK20170225] ; China Postdoctoral Science Foundation[2017M611026]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000470720700005
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Document Type期刊论文
Corresponding AuthorGarcia-Ramos, Felipe
Affiliation1.Univ Autonoma San Luis Potosi, Inst Fis, Manuel Nava 6, Slp 78290, Mexico
2.Catedras CONACyT, Av Insurgentes Sur 1582, Mexico City 03940, DF, Mexico
3.Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China
4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
5.Hefei Univ Technol, Sch Math, Hefei 230009, Anhui, Peoples R China
Recommended Citation
GB/T 7714
Garcia-Ramos, Felipe,Li, Jie,Zhang, Ruifeng. When is a dynamical system mean sensitive?[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS,2019,39:1608-1636.
APA Garcia-Ramos, Felipe,Li, Jie,&Zhang, Ruifeng.(2019).When is a dynamical system mean sensitive?.ERGODIC THEORY AND DYNAMICAL SYSTEMS,39,1608-1636.
MLA Garcia-Ramos, Felipe,et al."When is a dynamical system mean sensitive?".ERGODIC THEORY AND DYNAMICAL SYSTEMS 39(2019):1608-1636.
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