Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (5): 1142-1150.

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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)

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

CLC Number: 

  • O174.5
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