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June 2016 A sharp smoothness of the conjugation of class P-homeomorphisms to diffeomorphisms
Abdelhamid Adouani, Habib Marzougui
Kodai Math. J. 39(2): 425-438 (June 2016). DOI: 10.2996/kmj/1467830148

Abstract

Let f be a class P-homeomorphism of the circle. We prove that there exists a piecewise analytic homeomorphism that conjugate f to a one-class P with prescribed break points lying on pairwise distinct orbits. As a consequence, we give a sharp estimate for the smoothness of a conjugation of class P-homeomorphism f of the circle satisfying the (D)-property (i.e. the product of f-jumps in the break points contained in a same orbit is trivial), to diffeomorphism. When f does not satisfy the (D)-property the conjugating homeomorphism is never a class P and even more it is not absolutely continuous function when the total product of f-jumps in all the break points is non-trivial.

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Abdelhamid Adouani. Habib Marzougui. "A sharp smoothness of the conjugation of class P-homeomorphisms to diffeomorphisms." Kodai Math. J. 39 (2) 425 - 438, June 2016. https://doi.org/10.2996/kmj/1467830148

Information

Published: June 2016
First available in Project Euclid: 6 July 2016

zbMATH: 1365.37022
MathSciNet: MR3520523
Digital Object Identifier: 10.2996/kmj/1467830148

Rights: Copyright © 2016 Tokyo Institute of Technology, Department of Mathematics

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Vol.39 • No. 2 • June 2016
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