有限个线段映射的笛卡尔乘积的局部变差增长与局部拓扑熵
Pointwise Variation Growth and Entropy of the Descartes Product of a Few of Interval Maps
摘要
本文把线段映射的局部变差增长的概念推广到k维空间上的连续自映射的情形,其中iI为闭区间与局部拓扑熵映射均是上半连续的,得到一个与线段映射的变分原理相对应的变分原理。也得到了线段映射相应结果的一个推广。
出处
《理论数学》
2011年第3期184-188,共5页
Pure Mathematics
基金
广东自然科学基金博士启动项目(10452408801004217)
湛江市科技攻关项目(2010C3112005)。
二级参考文献10
-
1Walters P.,An introduction to ergodic theory,Graduate Texts in Mathematics 79,New York:Springer-Verlag,1982.
-
2Katok A.and Hasselblatt B.,Introduction to the modern theory of dynamical systems,Cambridge:Cambridge University Press,Cambridge UK,1995.
-
3Chen G.,Huang T.and Huang Y.,Chaotic behavior of interval maps and total variations of iterates,Int.J.Bifurc.& Chaos.,2004,14:2161-2186.
-
4Misiurewcz M.and Szlenk W.,Entropy of piecewise monotone maps,Studia Math.,1980,67:45-63.
-
5Preston C.,Iterates of piecewise monotone mappings on an interval,Lecture Notes in Mathematics 1347,Berlin,Heidelberg:Springer-Verlag,1988.
-
6Chen G.,Hsu S.B.and Huang T.,Analyzing displacement term's memory effect in a vander Pol type boundary condition to prove chaotic vibration of the wave equation,Int.J.Bifur.& Cahos.,2002,12:965-981.
-
7Chen G.,Huang T.,Juang J.and Ma D.,Unbounded growth of total variations of snapshots of the 1D linear wave equation due to the chaotic behavior of iterates of composite nonlinear boundary reflection relations,G.Chen et al ed.,in "Control of Nonlinear Distributed Parameter Systems",New York:Marcel Dekker Lecture Notes on Pure & Appl.Math.,2001,15-43.
-
8Huang Y.,Growth rates of total variations of snapshots of the 1D linear wave equation with composite nonlinear boundary reflection,Int.J.Bifurc.& Chaos.,2003,13:1183-1196.
-
9Block L.S.and Coppel W.A.,Dynamics in one dimension,Lecture Notes in Mathematics 1513,Berlin,Heidelberg:Springer-Verlag,1992.
-
10Brin M.and Katok A.,On local entropy,"Geometric Dynamics",30-38,Lecture Notes in Mathematics 1007,Berlin,New York,Tokyo:Springer-Verlag,1983.
-
1易建新.拓扑熵等于零的若干充分条件[J].西北师范大学学报(自然科学版),1989,25(4):7-9.
-
2董镇喜.探索复杂性的一些动力系统方法(Ⅱ)[J].系统工程理论与实践,1988,8(2):69-74.
-
3刘相驿,贾琪,李成平.有界变差函数的应用探讨[J].科教导刊,2018(21):29-29.
-
4鲜永菊,夏诚,徐昌彪.新混沌系统及其分数阶系统的自适应同步控制[J].控制理论与应用,2018,35(6):878-886. 被引量:14
-
5张丁文,陈占龙,谢忠.矩形方向约束的邻域空间推理[J].武汉大学学报(信息科学版),2018,43(8):1185-1192. 被引量:1