关于超空间非自治动力系统混沌的研究  

Research on Chastity in Hyperspace Non-Autonomous Systems

作　　者：冷震北 罗飞 高瑾[3] LENG Zhenbei;LUO Fei;GAO Jin(School of Mathematics and Computer Science,Chongqing College of International Business and Economics,Chongqing 401520;College of Mathematics and Statistics,Sichuan University of Science&Engineering,Zigong Sicuan 643000;School of Mathematics Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆对外经贸学院数学与计算机学院,重庆合川401520 [2]四川轻化工大学数学与统计学院,四川自贡643000 [3]重庆师范大学数学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2022年第5期104-109,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11471061);桥梁无损检测与工程计算四川省高校重点实验室项目(No.2022QZJD2,No.2021QYJ07)。

摘　　要：【目的】研究超空间非自治动力系统的混沌性质。【方法】通过一致收敛方法对非自治系统混沌性质进行研究。【结果】得到对任意k≥2,序列映射{f^(k)_(n)}^(∞)_(n=1)一致收敛于f^(k)。在此基础上,讨论了超空间非自治动力系统Li-Yorke混沌和初值敏感性的乘积系统,对任意正整数k:1)若(κ(X),f^([k])_(1,∞))和(κ(Y),g^([k])_(1,∞))是Li-Yorke混沌,则(κ(X×Y),f^([k])_(1,∞)×g^([k])_(1,∞))是Li-Yorke混沌。2)(κ(X×Y),f^([k])_(1,∞)×g^([k])_(1,∞))具有初值依赖敏感性当且仅当(κ(X),f^([k])_(1,∞))或(κ(Y),g^([k])_(1,∞))具有初值依赖敏感性。【结论】通过对超空间非自治系统的研究,进一步丰富了超空间中非自治系统混沌性质。[Purposes]The based space non-autonomous dynamic system is an important topic in recent years, and the chaotic nature of hyperspace non-autonomous dynamic system is also very important. [Methods]It uses uniform convergence and strong uniform convergence methods to study the chaotic properties of non-autonomous systems. [Findings]It is obtained that the mapping {f^(k)_(n)}^(∞)_(n=1) converges to f^(k) uniformly for any iteration index k≥2. On this basis, the product system of hyperspace non-autonomous dynamic system Li-Yorke chaos and initial value sensitivity is discussed: for any positive integer k: 1) If (κ(X),f^([k])_(1,∞)) and (κ(Y),g^([k])_(1,∞)) are Li-Yorke chaos, then (κ(X×Y),f^([k])_(1,∞)×g^([k])_(1,∞)) is also Li-Yorke chaos. 2)(κ(X×Y),f^([k])_(1,∞)×g^([k])_(1,∞))has initial value-dependent sensitivity if and only if (κ(X),f^([k])_(1,∞)) or (κ(Y),g^([k])_(1,∞)) has initial value-dependent sensitivity. [Conclusions]Through the study of hyperspace non-autonomous systems, it further enriches the chaotic nature of non-autonomous systems in hyperspace.

关 键 词：超空间 非自治动力系统 LI-YORKE混沌 Li-Yorke初值敏感 

分 类 号：O189.1[理学—数学]