Liousse, Isabelle PL homeomorphisms of the circle which are piecewise \(C^1\) conjugate to irrational rotations. (English) Zbl 1136.37333 Bull. Braz. Math. Soc. (N.S.) 35, No. 2, 269-280 (2004). Summary: For a PL homeomorphism \(f\) with irrational rotation number \(\alpha\), the following properties are equivalent:(i) \(f\) is conjugate to the rotation by \(\alpha\) through a piecewise \(C^1\) homeomorphism,(ii) the number of break points of \(f^n\) is bounded by some constant that doesn’t depend on \(n\),(iii) \(f\) is conjugate to an affine 2-intervals exchange transformation (with rotation number \(\alpha\)) through a PL homeomorphism,(iv) \(f\) is conjugate to the rotation by \(\alpha\) through a piecewise analytic homeomorphism. Cited in 9 Documents MSC: 37E10 Dynamical systems involving maps of the circle 37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems PDFBibTeX XMLCite \textit{I. Liousse}, Bull. Braz. Math. Soc. (N.S.) 35, No. 2, 269--280 (2004; Zbl 1136.37333) Full Text: DOI