Geodesic
Piecewise-smooth circle homeomorphisms with several break points
Izvestiya. Mathematics , Tome 76 (2012) no. 1, pp. 94-112.

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We prove that the invariant probability measure of an ergodic piecewise-smooth circle homeomorphism with several break points and the product of the jumps at break points non-trivial is singular with respect to Lebesgue measure.
Keywords: circle homeomorphism, rotation number, invariant measure. 
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A. A. Dzhalilov; D. Mayer; U. A. Safarov. Piecewise-smooth circle homeomorphisms with several break points. Izvestiya. Mathematics , Tome 76 (2012) no. 1, pp. 94-112. http://geodesic.mathdoc.fr/item/IM2_2012_76_1_a3/

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