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DYNAMICS ON SENSITIVE AND EQUICONTINUOUS FUNCTIONS
Li, Jie1,2; Yu, Tao3,4; Zeng, Tiaoying5,6
2018-06-01
Source PublicationTOPOLOGICAL METHODS IN NONLINEAR ANALYSIS
ISSN1230-3429
Volume51Issue:2Pages:545-563
AbstractThe notions of sensitive and equicontinuous functions under semigroup action are introduced and intensively studied. We show that a transitive system is sensitive if and only if it has a sensitive pair if and only if it has a sensitive function. While there exists a minimal non-weakly mixing system such that every non-constant continuous function is sensitive, and a topological dynamical system is weakly mixing if and only if it is sensitive consistently with respect to (at least) any two non-constant continuous functions. We also get a dichotomy result for minimal systems - every continuous function is either sensitive or equicontinuous.
KeywordSensitivity sensitive pairs sensitive functions equicontinuous functions weak mixing
DOI10.12775/TMNA.2017.054
Language英语
Funding ProjectNSF of Jiangsu Province[BK20170225] ; Science Foundation of Jiangsu Normal University[17XLR011] ; NNSF of China[11701231] ; NNSF of China[11371339] ; NNSF of China[11571335] ; China Postdoctoral Science Foundation[2017M611026]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000441425700010
PublisherJULIUSZ SCHAUDER CTR NONLINEAR STUDIES
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30780
Collection中国科学院数学与系统科学研究院
Affiliation1.Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200433, Peoples R China
4.Univ Sci & Technol China, Dept Math, Chinese Acad Sci, Wu Wen Tsun Key Lab Math, Hefei 230026, Anhui, Peoples R China
5.Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R China
6.Jiaying Univ, Sch Math, Meizhou 514015, Guangdong, Peoples R China
Recommended Citation
GB/T 7714
Li, Jie,Yu, Tao,Zeng, Tiaoying. DYNAMICS ON SENSITIVE AND EQUICONTINUOUS FUNCTIONS[J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS,2018,51(2):545-563.
APA Li, Jie,Yu, Tao,&Zeng, Tiaoying.(2018).DYNAMICS ON SENSITIVE AND EQUICONTINUOUS FUNCTIONS.TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS,51(2),545-563.
MLA Li, Jie,et al."DYNAMICS ON SENSITIVE AND EQUICONTINUOUS FUNCTIONS".TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS 51.2(2018):545-563.
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