### 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 language | English |
---|---|

Pages (from-to) | 347-359 |

Number of pages | 13 |

Journal | Malaysian Journal of Mathematical Sciences |

Volume | 10 |

Publication status | Published - 2016 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Malaysian Journal of Mathematical Sciences*,

*10*, 347-359.

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

Research output: Contribution to journal › Article

*Malaysian Journal of Mathematical Sciences*, vol. 10, pp. 347-359.

}

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

AN - SCOPUS:85012285133

VL - 10

SP - 347

EP - 359

JO - Malaysian Journal of Mathematical Sciences

JF - Malaysian Journal of Mathematical Sciences

SN - 1823-8343

ER -