On invariant probability measure of a piecewise-smooth circle homeomorphism of Zygmund class

H. Akhadkulov, Mohd. Salmi Md. Noorani, S. Akhatkulov

Research output: Contribution to journalArticle

Abstract

We show that the invariant probability measure of the ergodic piecewisesmooth circle homeomorphisms with several break points which satisfy Zygmund condition and the product of jumps at break points non-trivial is singular with respect to Lebesgue measure.

Original languageEnglish
Pages (from-to)347-359
Number of pages13
JournalMalaysian Journal of Mathematical Sciences
Volume10
Publication statusPublished - 2016

Fingerprint

Homeomorphism
Invariant Measure
Probability Measure
Circle
Lebesgue Measure
Jump
Class

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On invariant probability measure of a piecewise-smooth circle homeomorphism of Zygmund class. / Akhadkulov, H.; Md. Noorani, Mohd. Salmi; Akhatkulov, S.

In: Malaysian Journal of Mathematical Sciences, Vol. 10, 2016, p. 347-359.

Research output: Contribution to journalArticle

@article{cad88c4952304b91835aad0ca6fcfb3c,
title = "On invariant probability measure of a piecewise-smooth circle homeomorphism of Zygmund class",
abstract = "We show that the invariant probability measure of the ergodic piecewisesmooth circle homeomorphisms with several break points which satisfy Zygmund condition and the product of jumps at break points non-trivial is singular with respect to Lebesgue measure.",
keywords = "Break point, Circle homeomorphism, Invariant measure, Rotation number",
author = "H. Akhadkulov and {Md. Noorani}, {Mohd. Salmi} and S. Akhatkulov",
year = "2016",
language = "English",
volume = "10",
pages = "347--359",
journal = "Malaysian Journal of Mathematical Sciences",
issn = "1823-8343",
publisher = "Institute for Mathematical Research",

}

TY - JOUR

T1 - On invariant probability measure of a piecewise-smooth circle homeomorphism of Zygmund class

AU - Akhadkulov, H.

AU - Md. Noorani, Mohd. Salmi

AU - Akhatkulov, S.

PY - 2016

Y1 - 2016

N2 - We show that the invariant probability measure of the ergodic piecewisesmooth circle homeomorphisms with several break points which satisfy Zygmund condition and the product of jumps at break points non-trivial is singular with respect to Lebesgue measure.

AB - We show that the invariant probability measure of the ergodic piecewisesmooth circle homeomorphisms with several break points which satisfy Zygmund condition and the product of jumps at break points non-trivial is singular with respect to Lebesgue measure.

KW - Break point

KW - Circle homeomorphism

KW - Invariant measure

KW - Rotation number

UR - http://www.scopus.com/inward/record.url?scp=85012285133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85012285133&partnerID=8YFLogxK

M3 - Article

VL - 10

SP - 347

EP - 359

JO - Malaysian Journal of Mathematical Sciences

JF - Malaysian Journal of Mathematical Sciences

SN - 1823-8343

ER -