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

• 论文 • 上一篇    下一篇

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. 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 Cheng2,*(),Shanshuang Yang3()   

  1. 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:

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