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Dynamical Systems
An International Journal
Volume 27, 2012 - Issue 2
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Original Articles

On piecewise smoothness of conjugacy of class P circle homeomorphisms to diffeomorphisms and rotations

Abdelhamid Adouani Faculty of Science of Bizerte, Department of Mathematics, University of Carthage, Zarzouna 7021, Tunisia
&
Habib Marzougui Faculty of Science of Bizerte, Department of Mathematics, University of Carthage, Zarzouna 7021, TunisiaCorrespondence[email protected]
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Pages 169-186 | Received 28 Oct 2010, Accepted 21 Oct 2011, Published online: 08 Dec 2011

References

  • Poincaré , H . 1885 . Oeuvres complètes, t. , 1 : 137 – 158 .
  • Denjoy , A . 1932 . Sur les courbes définies par les équations différentielles à la surface du tore . J. Math. Pures Appl. , 11 : 333 – 375 .
  • Arnold , VI . 1961 . Small denominators I; on the mapping of a circle into itself . Akad. Nauk, Serie Math. , 25 ( 1 ) : 21 – 96 . (Transl. A.M.S., 2nd Serie, 46, pp. 213–284)
  • Boshernitzan , MD . 1993 . Dense orbits of rationals . Proc. Am. Math. Soc. , 117 ( 4 ) : 1201 – 1203 .
  • Herman , M . 1979 . Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations . Pub. Math. Inst. Hautes Etudes Sci. , 49 : 5 – 234 .
  • Katznelson , Y and Ornstein , D . 1989 . The differentiability of the conjugation of certain diffeomorphisms of the circle . Ergod. Theory Dyn. Syst. , 9 ( 4 ) : 643 – 680 .
  • Khanin , KM and Sinaĭ , YaG . 1989 . Smoothness of conjugacies of diffeomorphisms of the circle with rotations . Russ. Math. Surveys , 44 ( 1 ) : 69 – 99 .
  • Khanin , KM and Teplinskyi , A . 2009 . Herman's theory revisited . Invent. Math. , 178 : 333 – 344 .
  • Yoccoz , JC . Il n' y a pas de contre-exemple de Denjoy analytique, C.R.A.S., Série I, 298(7) (1984), pp. 141–144
  • Hawkins , J and Schmidt , K . 1982 . On C 2-diffeomorphisms of the circle which are of type III . Invent. Math. , 66 : 511 – 518 .
  • Liousse , I . 2005 . PL homeomorphisms of the circle which are piecewise C 1 conjugate to irrational rotations . Bull. Braz. Math. Soc. New Series , 35 ( 2 ) : 269 – 280 .
  • Dzhalilov , AA . 1999 . Piecewise smoothness of conjugate homeomorphisms of a circle with corners . Theor. Math. Phys. , 120 ( 2 ) : 961 – 972 .
  • Adouani , A and Marzougui , H . 2008 . Sur les Homéomorphismes du cercle de classe PC r par morceaux (r ≥ 1) qui sont conjugués C r par morceaux aux rotations irrationnelles . Ann. Inst. Fourier , 58 ( 3 ) : 755 – 775 .
  • Liousse , I . 2008 . Rotation numbers in Thompson–Stein groups and applications . Geom. Dedicata , 131 : 49 – 71 .
  • Minakawa , H . 1997 . Classification of exotic circles of PL+(S1) . Hokkaido Math. J. , 26 ( 3 ) : 685 – 697 .
  • Adouani , A and Marzougui , H . Computation of rotation numbers for a class of PL-circle homeomorphisms, Discret. Contin. Dyn. Syst. (2011), under revision

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