多项式粗糙熵及其若干性质研究  

Research on Polynomial Coarse Entropy and Its Properties

作　　者：王威 梁雅丽 张俊杰 黄萍 WANG Wei;LIANG Yali;ZHANG Junjie;HUANG Ping(School of General Education,Nantong Institute of Technology,Nantong 226002,China;School of Tourism,Shanghai Normal University,Shanghai 201418,China;Shanghai Institute of Tourism,Shanghai 201418,China;School of Mathematics Sciences,Suzhou University of Science and Technology,Suzhou 215009,China;School of Mathematical and Physical Sciences,Taizhou University,Taizhou 225300,China)

机构地区：[1]南通理工学院基础教学学院,江苏南通226002 [2]上海师范大学旅游学院,上海201418 [3]上海旅游高等专科学校,上海201418 [4]苏州科技大学数学科学学院,江苏苏州215009 [5]泰州学院数理学院,江苏泰州225300

出　　处：《安阳师范学院学报》2025年第2期1-4,70,共5页Journal of Anyang Normal University

基　　金：国家自然科学基金项目(项目编号:12101446);上海市“晨光计划”项目(项目编号:20CGB09);2023南通理工学院科研项目“动力系统中熵的研究”(项目编号:2022xk(z)43);江苏省研究生科研创新计划项目(项目编号:KYCX23_3300)。

摘　　要：伪轨对动力系统的定性研究起着非常重要的作用,而粗糙熵则是从粗糙的观点下研究动力系统。利用伪轨性质和R-生成集定义了多项式粗糙熵,并在假设L是严格递增情况下讨论了粗糙熵的性质,类似于多项式拓扑熵,多项式粗糙熵是用来测量粗糙熵为零的轨道性质。Pseudo orbit plays a very important role in the qualitative study of dynamical systems,while coarse entropy studies dynamical systems from a rough perspective.We defined polynomial coarse entropy using the pseudo orbital property and R–generator set,and discussed the properties of coarse entropy under the assumption of strict increasing similar to polynomial topological entropy.Polynomial coarse entropy is used to measure the properties of orbits with zero coarse entropy.

关 键 词：拓扑熵 多项式熵 粗糙熵 

分 类 号：O189[理学—数学]