迭代函数系统的拓扑传递性质  

Topological Transitive Properties of Iterated Function System

作　　者：方俊炎 钟新林 FANG Junyan;ZHONG Xinlin(School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《新乡学院学报》2021年第12期9-12,共4页Journal of Xinxiang University

摘　　要：研究了由矩阵A所决定的迭代函数系统(X,F_(A))中关于拓扑熵的性质,证明了斜积变换F_(A)的拓扑熵h(F_(A))等于log_(A)ρ_(A)(a≥e)与h(F_(A))之和,其中ρ_(A)是A的谱半径,h(F_(A))是(X,F_(A))的拓扑熵。当F_(A)中每个映射f_(i)∈F_(A)是半开映射时,证明了F_(A)是拓扑传递的当且仅当(X,F_(A))是拓扑传递的的结论。The properties of iterated function system(X,F_(A)) determined by matrix A are studied in this paper.The conclusion that h(F_(A)) is equal to the sum of log_(A)ρ_(A)and h(F_(A)) is obtained,where h(F_(A)) is the topological entropy of skew-product transformation,ρ_(A)is the spectral radius of A,h(F_(A)) is the topological entropy of(X,F_(A)).When every map f_(i)∈F_(A)is semi-open,the conclusion that F_(A) is topologically transmission if and only if(X,F_(A))is topologically transmission is obtained.

关 键 词：迭代函数系统 斜积变换 拓扑熵 谱半径 拓扑传递 

分 类 号：O189.11[理学—数学]