Geodesic
A note on the conjugacy between two critical circle maps
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 287-300

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We study a conjugacy between two critical circle homeomorphisms with irrational rotation number. Let $f_{i}, i=1,2$ be a $C^{3}$ circle homeomorphisms with critical point $x_{cr}^{(i)}$ of the order $2m_{i}+1$. We prove that if $2m_{1}+1 \neq 2m_{2}+1$, then conjugating between $f_{1}$ and $f_{2}$ is a singular function.
Keywords: circle homeomorphism, critical point, conjugating map, rotation number, singular function. 
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     title = {A note on the conjugacy between two critical circle maps},
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     volume = {14},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_3_a2/}
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Utkir A. Safarov. A note on the conjugacy between two critical circle maps. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 287-300. http://geodesic.mathdoc.fr/item/JSFU_2021_14_3_a2/