Konstantin Khanin, Sasa Kocic
Rigidity of cyclic generalized interval exchange transformations
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ABSTRACT.  For almost all irrational rho\in(0,1), any two cyclic generalized interval exchange transformations, with breaks on the same orbit, with the same rotation number rho and the same size of the corresponding breaks, are C^1-smoothly conjugate to each other. In particular, for almost all irrational rho\in(0,1), generalized interval exchange transformations of two intervals, with the same rotation number rho and the same size of the corresponding breaks, are C^1-smoothly conjugate to each other. These results generalize the results of Marmi, Moussa and Yoccoz [8].