一个Lebesgue稠密定理在动力系统中的推广  

A Generalization of Lebesgue Density Theorem in Dynamical Systems

作　　者：张俊杰 孙浩宇 王威 ZHANG Junjie;SUN Haoyu;WANG Wei(School of Mathematical Sciences,Suzhou University of Science and Technology,215009,Suzhou,Jiangsu,China;School of General Education,Nantong Institute of Technology,226002,Nantong,Jiangsu,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009 [2]南通理工学院基础教学学院,江苏南通226002

出　　处：《淮北师范大学学报（自然科学版）》2023年第4期10-14,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：国家自然科学基金(11971236);南通理工学院中青年骨干教师(ZQNGGJS202135);江苏省研究生科研创新计划(KYCX23_3300)。

摘　　要：文章将其他收缩集族代替经典的欧几里得球族,验证其对应的Lebesgue稠密定理。利用系统的可扩张性和有界性变形等动力系统工具,研究离散动力系统生成的动力系统球族的几何及测度性质,结果表明:其他收缩集族所对应的Lebesgue稠密定理仍然成立。In this paper,the classical Euclideam spere family is replaced by other families of contracted sets,and the correspording Lebesgue density theorem is verified.Using the systematic tools such as the expansion of the system and boundary deformation to study the geometry and measurement properties of the power sys⁃tem balls generated by the discrete power system,the result shows that the dense theorem of the Lebesgue corresponding to other contracted centers is still established.

关 键 词：Lebesgue稠密定理 动力系统 微分同胚 扩张性 

分 类 号：O171[理学—数学] O193[理学—基础数学]