Conjugations between circle maps with a single break point

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:366

Article

Dzhalilov, Akhtam²  Akin, Hasan¹  Temir, Seyit³ 

[1] Zirve Univ, Fac Educ, TR-27260 Gaziantep, Turkey

[2] Samarkand State Univ, Fac Math, Samarkand 703004, Uzbekistan

[3] Harran Univ, Art & Sci Fac, Dept Math, TR-63200 Sanliurfa, Turkey

关键词: Circle homeomorphism;    Break points;    Rotation number;    Invariant measures;    Singular function;   

DOI  :  10.1016/j.jmaa.2009.12.050

来源: Elsevier

【 摘 要 】

Consider two circle homeomorphisms f(i) is an element of C2+alpha (S\{b(i)}), alpha > 0. i = 1, 2 with a single break point b(i) i.e. a discontinuity in the derivative Df(i), and identical irrational rotation number rho. Suppose the jump ratios sigma(1) = Df(1)(b(1)-0)/Df(1)(b(1)+0) and sigma(2) = Df(1)(b(2)-0)/Df(2)(b(2)+0) do not coincide. Then the map psi conjugating f(1) and f(2) is a singular function i.e. it is continuous on S-1 and D psi(x) = 0 a.e. with respect to LebeSgUe measure. (C) 2009 Elsevier Inc. All rights reserved.

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