A necessary condition for the absolute continuity of invariant measure of circle maps with countably infinite number of break points

Habibulla Akhadkulov, Azizan Bin Saaban, Mohd. Salmi Md. Noorani, Sokhobiddin Akhatkulov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let f be a circle homeomorphism with countably many break points that is, differentiable except in countably many points where the derivatives have a jump. Assuming its rotation number ρ to be irrational, we provide a necessary condition for the absolute continuity of invariant measure with respect to the Lebesgue measure.

Original languageEnglish
Pages (from-to)675-688
Number of pages14
JournalFar East Journal of Mathematical Sciences
Volume101
Issue number3
DOIs
Publication statusPublished - 1 Feb 2017

Fingerprint

Circle Map
Absolute Continuity
Invariant Measure
Necessary Conditions
Rotation number
Homeomorphism
Lebesgue Measure
Differentiable
Jump
Circle
Derivative

Keywords

  • Absolute continuity
  • Break point
  • Circle homeomorphism
  • Invariant measure
  • Rotation number

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A necessary condition for the absolute continuity of invariant measure of circle maps with countably infinite number of break points. / Akhadkulov, Habibulla; Saaban, Azizan Bin; Md. Noorani, Mohd. Salmi; Akhatkulov, Sokhobiddin.

In: Far East Journal of Mathematical Sciences, Vol. 101, No. 3, 01.02.2017, p. 675-688.

Research output: Contribution to journalArticle

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