Geodesic
Piecewise smoothness of conjugate homeomorphisms of a circle with corners
Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 2, pp. 179-192

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Homeomorphisms that are conjugate to some circle homeomorphisms with corners lying on one trajectory are piecewise-linear functions. 
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     author = {A. A. Dzhalilov},
     title = {Piecewise smoothness of conjugate homeomorphisms of a circle with corners},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--192},
     publisher = {mathdoc},
     volume = {120},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a0/}
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A. A. Dzhalilov. Piecewise smoothness of conjugate homeomorphisms of a circle with corners. Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 2, pp. 179-192. http://geodesic.mathdoc.fr/item/TMF_1999_120_2_a0/