### 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 language | English |
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Pages (from-to) | 675-688 |

Number of pages | 14 |

Journal | Far East Journal of Mathematical Sciences |

Volume | 101 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Feb 2017 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Far East Journal of Mathematical Sciences*,

*101*(3), 675-688. https://doi.org/10.17654/MS101030675

**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.

Research output: Contribution to journal › Article

*Far East Journal of Mathematical Sciences*, vol. 101, no. 3, pp. 675-688. https://doi.org/10.17654/MS101030675

}

TY - JOUR

T1 - A necessary condition for the absolute continuity of invariant measure of circle maps with countably infinite number of break points

AU - Akhadkulov, Habibulla

AU - Saaban, Azizan Bin

AU - Md. Noorani, Mohd. Salmi

AU - Akhatkulov, Sokhobiddin

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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.

KW - Absolute continuity

KW - Break point

KW - Circle homeomorphism

KW - Invariant measure

KW - Rotation number

UR - http://www.scopus.com/inward/record.url?scp=85011662389&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85011662389&partnerID=8YFLogxK

U2 - 10.17654/MS101030675

DO - 10.17654/MS101030675

M3 - Article

VL - 101

SP - 675

EP - 688

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

SN - 0972-0871

IS - 3

ER -