PL Homeomorphisms of the circle which are piecewise <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript> conjugate to irrational rotations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

PL Homeomorphisms of the circle which are piecewise C1 conjugate to irrational rotations

Authors:	Isabelle?Liousse author-information" > author-information__contact u-icon-before" > mailto:Isabelle.Liousse@agat.univ-lille.fr" title=" Isabelle.Liousse@agat.univ-lille.fr" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Laboratoire Paul Painlevé, U.M.R 8524 au C.N.R.S., U.F.R. de Mathématiques, Université Lille I, 59655 Villeneuve dAscq Cedex, FRANCE

Abstract:	For a PL homeomorphism f with irrational rotation number , the following properties are equivalent(i) f is conjugate to the rotation by through a piecewise C ¹ homeomorphism,(ii) the number of break points of f ⁿ is bounded by some constant that doesnt depend on n,(iii) f is conjugate to an affine 2-intervals exchange transformation (with rotation number ) through a PL homeomorphism,(iv) f is conjugate to the rotation by through a piecewise analytic homeomorphism.

Keywords:	PL Homeomorphisms of the circle invariant measure conjugacy
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