文献类型：期刊文献

英文题名：Sensitivity and Transitivity of Systems Satisfying the Large Deviations Theorem in a Sequence

作者：Li, Risong[1,2];Lu, Tianxiu[3,4];Waseem, Anwar[3]

机构：[1]Guangdong Ocean Univ, Sch Math & Comp Sci, Zhanjiang 610500, Guangdong, Peoples R China;[2]Bridge Nondestruct Detecting & Engn Comp Key Lab, Zigong 643000, Sichuan, Peoples R China;[3]Sichuan Univ Sci & Engn, Sch Math & Stat, Zigong 643000, Sichuan, Peoples R China;[4]Artificial Intelligence Key Lab Sichuan Prov, Zigong 643000, Sichuan, Peoples R China

年份：2019

卷号：29

期号：9

外文期刊名：INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

收录：SCI-EXPANDED(收录号：WOS:000483030700015)、、EI(收录号：20193607392288)、Scopus(收录号：2-s2.0-85071579108)、WOS

基金：This project was supported by the National Natural Science Foundation of China (Nos. 11501391, 61573010 and 11701397), the Opening Project of Artificial Intelligence Key Laboratory of Sichuan Province (No. 2018RZJ03) and the Opening Project of Bridge Non-destruction Detecting and Engineering Computing Key Laboratory of Sichuan Province (2018QZJ03).

语种：英文

外文关键词：Large deviations theorem in a sequence; sensitivity; syndetic sensitivity; ergodic sensitivity

外文摘要：Let h : F -> F be a continuous selfmap of a nontrivial compact metric space (F, rho). This paper derives the large deviations theorem in a sequence. It is shown that if (h, eta) satisfies the large deviations theorem in a sequence then it is an E-system which implies that h is syndetically transitive, and that if the pair (h, eta) satisfies the large deviations theorem in a sequence and F is an infinite space, then h is syndetically sensitive, which implies that h is ergodically sensitive. Moreover, it is proved that if the pair (h, eta) satisfies the large deviations theorem in a syndetic sequence, then eta is an ergodic measure with supp(eta) = F. Our main results extend and improve the corresponding results in the literature.