多项式型迭代方程不连续解的构造（英文）  

On Construction of Discontinuous Solutions for the Polynomial-like Iterative Equation

作　　者：刘敬华 Liu Jinghua(School of Mathematics and StatisticsLingnan Normal University,Guangdong Zhanjiang 524048)

机构地区：[1]岭南师范学院数学与统计学院,广东湛江524048

出　　处：《长江大学学报（自然科学版）》2018年第21期35-42,78,共9页Journal of Yangtze University(Natural Science Edition)

基　　金：NSFC(11661017);The General Item of Lingnan Normal University(ZL1505);KSP of Lingnan Normal University(1171518004)

摘　　要：在动力系统的研究中,对多项式型迭代方程解的研究是一个重要的课题。因为该问题与数据的修复和某个系统的不变流形有密切关系,所以其连续和半连续解得到广泛关注并得到了一些经典的结论。研究了多项式型迭代方程的不连续解:首先将不连续函数分成5类,然后对每一个子类利用延拓的方法构造出其通解。最后,将所得的结论运用到了迭代根的求解。Studying the solutions of the polynomial-like iterative equation is a significant subject in the research of dynamical systems because it closely relates to the data recovery and the invariant manifolds of systems.Much effort has been made to investigate its continuous and semicontinuous solutions,and many results are obtained.In this paper,firstly,we classify discontinuous self-maps into five subcases,and then with an extension method we give a general construction of discontinuous solutions of the polynomial-like iterative equation for each subcase.At last we apply main results to iterative roots.

关 键 词：多项式型迭代方程 不连续解 迭代根 

分 类 号：O171[理学—数学]