同胚映射的代数指数、Hölder指数和拟对称指数

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1142-1150.

同胚映射的代数指数、Hölder指数和拟对称指数

杨存基¹(),程涛^2,*(),杨善双³()

¹ 大理大学数学与计算机学院云南大理 671000
² 华东师范大学数学科学学院上海 200241
³ 埃默里大学数学系美国佐治亚州亚特兰大 30322

收稿日期:2019-01-15 出版日期:2020-10-26 发布日期:2020-11-04
通讯作者: 程涛 E-mail:kmycj@126.com;tcheng@math.ecnu.edu.cn;syang05@emory.edu
作者简介:杨存基, E-mail:kmycj@126.com|杨善双, E-mail:syang05@emory.edu
基金资助:
国家自然科学基金(11861005);国家自然科学基金(11871215);上海市核心数学与实践重点实验室基金(18dz2271000)

Algebraic, Hölder and Quasisymmetric Exponents of a Homeomorphism

Cunji Yang¹(),Tao Cheng^2,*(),Shanshuang Yang³()

¹ Department of Mathematics and Computer, Dali University, Yunnan Dali 671003
² School of Mathematical Sciences, East China Normal University, Shanghai 200241
³ Department of Mathematics, Emory University, Atlanta, GA 30322, USA

Received:2019-01-15 Online:2020-10-26 Published:2020-11-04
Contact: Tao Cheng E-mail:kmycj@126.com;tcheng@math.ecnu.edu.cn;syang05@emory.edu
Supported by:
the NSFC(11861005);the NSFC(11871215);the Science and Technology Commission ofShanghai Municipality(18dz2271000)

摘要/Abstract

摘要：

给定实轴上的同胚映射，定义了拟对称指数、代数指数和Hölder指数.上述指数刻画了同胚映射的局部特征，同时在拟对称映射和拟共形映射的研究中具有重要作用.探索了三个指数的相互关系并给出了几个实例.

关键词: 拟共形映射, 拟对称指数, 代数指数, Hölder指数

Abstract:

Given a homeomorphism of the real line, we define its quasisymmetric exponent, Hölder exponent and algebraic exponent. These exponents capture the local behavior of a homeomorphism and are useful in the study of quasisymmetric maps and quasiconformal maps. In this paper we shall explore the relations among these exponents and give some examples.

Key words: Quasiconformal map, Quasisymmetric exponent, Hölder exponent, Algebraic exponent

中图分类号:

O174.5

杨存基,程涛,杨善双. 同胚映射的代数指数、Hölder指数和拟对称指数[J]. 数学物理学报, 2020, 40(5): 1142-1150.

Cunji Yang,Tao Cheng,Shanshuang Yang. Algebraic, Hölder and Quasisymmetric Exponents of a Homeomorphism[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1142-1150.

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