迭代函数方程的同胚解

摘要/Abstract

摘要：

已有的迭代函数方程解结论主要是关于它的连续性和光滑性. 然而在函数方程与动力系统的共轭和线性化理论研究中, 解的同胚性质起到重要作用. 对这一问题虽然已取得部分结论, 但还未有一个完整的描述. 该文首先利用构造和逼近的方法考虑一般类型的迭代函数方程的同胚解, 然后将得到的结论应用到研究多项式型迭代方程.

关键词: 迭代函数方程, 同胚解, 局部线性函数, 一致收敛, 齐次函数

Abstract:

Most known results on the solutions of iterative functional equations are about their continuity and smoothness. However, concerning the study of conjugation and linearization in functional equations and dynamical systems, the property of homeomorphism play an important role in these theories. Although partial results were obtained, a full description is still open. In this paper, we first consider homeomorphic solutions to a general iterative functional equation by the methods of construction and approximation. Then, the obtained results are used to study the solutions of polynomial-like iterative functional equations.

Key words: Iterative equation, Homeomorphic solution, Locally linear function, Uniform convergence, Homogeneous function

中图分类号:

O175.23

刘敬华, 李林. 迭代函数方程的同胚解[J]. 数学物理学报, 2024, 44(2): 313-325.

Liu Jinghua, Li Lin. Homeomorphic Solutions of Iterative Functional Equations[J]. Acta mathematica scientia,Series A, 2024, 44(2): 313-325.

图/表 10

图 1

$F\in\mathcal{R}^{\xi}[J]$ "

图 1

图 2

$F\in\mathcal{S}^{\zeta}[J]$ "

图 2

图 3

$F\in\mathcal{R}[J]$ "

图 3

图 4

$F\in\mathcal{S}[J]$ "

图 4

图 5

$F\in\mathcal{W}^{\xi}[I]$ "

图 5

图 6

$F\in\mathcal{V}^{\zeta}[I]$ "

图 6

图 7

$F\in\mathcal{W}[I]$ "

图 7

图 8

$F\in\mathcal{V}[I]$ "

图 8

图 9

$F\in\mathcal{P}_{\alpha}^{\xi}[I]$ "

图 9

图 10

$F\in\mathcal{P}_{\alpha}[I]$ "

图 10

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