Yayınlanmış 1 Ocak 2010 | Sürüm v1
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Conjugations between circle maps with a single break point

  • 1. Samarkand State Univ, Fac Math, Samarkand 703004, Uzbekistan
  • 2. Zirve Univ, Fac Educ, TR-27260 Gaziantep, Turkey
  • 3. Harran Univ, Art & Sci Fac, Dept Math, TR-63200 Sanliurfa, Turkey

Açıklama

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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