Geodesic
The H\"older property of singular invariant measures of circle homeomorphisms with single corners
Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 3, pp. 355-366

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Any circle homeomorphism with a corner has an invariant measure that is singular w.r.t. the Lebesgue measure. It is proved that the singularity of the invariant measure has the Hölder property. 
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     author = {A. A. Dzhalilov},
     title = {The {H\"older} property of singular invariant measures of circle homeomorphisms with single corners},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--366},
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     volume = {121},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a0/}
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A. A. Dzhalilov. The H\"older property of singular invariant measures of circle homeomorphisms with single corners. Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 3, pp. 355-366. http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a0/