Geodesic
Invariant measure of circle maps with mixed type of singularities
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 71-84

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In this paper we consider the critical circle homeomorphisms with several break points. It is well known that a circle homeomorphisms $f$ with irrational rotation number $\rho$ is strictly ergodic, i.e. it has a unique $f$ –invariant probability measure $\mu$. We prove that invariant measure of critical circle homeomorphisms with finite number of break points is singular w.r.t Lebegue measure.
Keywords: Circle homeomorphisms, invariant measure, rotation number, break point, critical point, singular measure. 
@article{IVM_2023_7_a7,
     author = {U. A. Safarov},
     title = {Invariant measure of circle maps with mixed type of singularities},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {71--84},
     publisher = {mathdoc},
     number = {7},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_7_a7/}
}
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U. A. Safarov. Invariant measure of circle maps with mixed type of singularities. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 71-84. http://geodesic.mathdoc.fr/item/IVM_2023_7_a7/