On the Singularity of the Conjugation Between Piecewise-Smooth Circle Homeomorphisms

Sokhobiddin Akhatkulov, Mohd. Salmi Md. Noorani

Research output: Contribution to journalArticle

Abstract

Let f1 and f2 be two orientation-preserving circle homeomorphisms with the same irrational rotation number ρ and each with a single break point b1 and b2, respectively. Suppose that the derivatives Df1 and Df2 satisfy a certain Zygmund condition except break points and the jumps σ(b1)=Df1(b1-0)Df1(b1+0), σ(b2)=Df2(b2-0)Df1(b2+0) do not coincide. Then the map ψ conjugating f1 and f2 is singular.

Original languageEnglish
Pages (from-to)1607-1622
Number of pages16
JournalBulletin of the Malaysian Mathematical Sciences Society
Volume41
Issue number3
DOIs
Publication statusPublished - 1 Jul 2018

Fingerprint

Conjugation
Circle
Singularity
Irrational number
Rotation number
Jump
Derivative

Keywords

  • Break point
  • Circle homeomorphism
  • Conjugation
  • Cross-ratio distortion
  • Rotation number

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the Singularity of the Conjugation Between Piecewise-Smooth Circle Homeomorphisms. / Akhatkulov, Sokhobiddin; Md. Noorani, Mohd. Salmi.

In: Bulletin of the Malaysian Mathematical Sciences Society, Vol. 41, No. 3, 01.07.2018, p. 1607-1622.

Research output: Contribution to journalArticle

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