C1-rigidity of circle maps with breaks for almost all rotation numbers
[La rigidité différentiable d'applications du cercle avec un point de singularité de type rupture pour presque tous les nombres de rotation]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 5, pp. 1163-1203.

Nous démontrons que pour presque tous les irrationnels ρ∈(0,1), deux difféomorphismes du cercle C2+α lisses, α∈(0,1), avec un point de singularité de type rupture où la dérivée a une discontinuité de saut, avec le même nombre de rotation ρ et la même taille de rupture c∈ℝ+∖{1}, sont C1-conjugués l'un à l'autre.

We prove that, for almost all irrational ρ∈(0,1), every two C2+α-smooth, α∈(0,1), circle diffeomorphisms with a break point, i.e., a singular point where the derivative has a jump discontinuity, with the same rotation number ρ and the same size of the break c∈ℝ+∖{1}, are C1-smoothly conjugate to each other.

Publié le :
DOI : 10.24033/asens.2342
Classification : 37E10, 37E20.
Keywords: Rigidity, conjugacy, circle maps, diffeomorphisms with a break
Mot clés : Rigidité, conjugaison, cartes de cercle, difféomorphismes avec des singularités de type rupture. 
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     title = {$C^1$-rigidity of circle maps with breaks  for almost all rotation numbers},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1163--1203},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 50},
     number = {5},
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     doi = {10.24033/asens.2342},
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Khanin, Konstantin; Kocić, Saša; Mazzeo, Elio. $C^1$-rigidity of circle maps with breaks  for almost all rotation numbers. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 5, pp. 1163-1203. doi : 10.24033/asens.2342. https://www.numdam.org/articles/10.24033/asens.2342/

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