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. 
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/
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     title = {Invariant measure of circle maps with mixed type of singularities},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2023_7_a7/}
}
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