文献类型：期刊文献

英文题名：Study on Strong Sensitivity of Systems Satisfying the Large Deviations Theorem

作者：Li, Risong[1];Lu, Tianxiu[2];Yang, Xiaofang[2];Jiang, Yongxi[2]

机构：[1]Guangdong Ocean Univ, Sch Math & Comp Sci, Zhanjiang 524025, Guangdong, Peoples R China;[2]Sichuan Univ Sci & Engn, Coll Math & Stat, Key Lab Higher Educ Sichuan Prov Enterprise Infor, Zigong 643000, Sichuan, Peoples R China

年份：2021

卷号：31

期号：10

外文期刊名：INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

收录：SCI-EXPANDED(收录号：WOS:000684604000013)、、EI(收录号：20213410799576)、Scopus(收录号：2-s2.0-85112866745)、WOS

基金：This work was supported by the Opening Project of Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things (No. 2020WZJ01), Ministry of Education Science and Technology Development center (No. 2020QT13) and Scientific Research Project of Sichuan University of Science and Engineering (No. 2020RC24).

语种：英文

外文关键词：Sensitivity; positive lower density sensitivity; topologically strong ergodicity; ergodic sensitivity

外文摘要：Let (S,tau) be a nontrivial compact metric space with metric tau and g : S -> S be a continuous self-map, B(S) be the sigma-algebra of Borel subsets of S, and nu be a Borel probability measure on (S,B(S)) with nu(V ) is an element of (0, +infinity) for any open subset V not equal null of S. This paper proves the following results: (1) If the pair (g,nu) has the property that for any beta > 0, there is r(beta) > 0 such that nu ({p is an element of S : 1/m Sigma(m-1)(i=0)chi(V)(g(i)(p)) integral X(V)d(nu) vertical bar > beta <= (e-mr(beta)), for any open subset V not equal null of S and all n >= 1 sufficiently large (where chi(V) is the characteristic function of the set V), then the following hold: (a) The map g is topologically ergodic. (b) The upper density mu over bar (Ng(p,V )) of Ng(p,V ) is positive for any open subset V not equal null of S, where Ng(p,V ) = {m is an element of{0, 1, ...} : gm(p) is an element of V }. (c) There is a g-invariant Borel probability measure nu having full support (i.e. supp(nu) = S). (d) Sensitivity of the map g implies positive lower density sensitivity, hence ergodical sensitivity. (2) If mu_(Ng(A,B)) = 1 for any two nonempty open subsets A,B, then there exists lambda > 0 satisfying mu_(Ng(C,lambda)) = 1 for any nonempty open subset C subset of S, where Ng(C,lambda) = {l is an element of{0, 1, horizontal ellipsis } : there exist a,b is an element of C with tau(gl(a),gl(b)) > lambda}.