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arXiv · 1508.03549

A sharp smoothness of the conjugation of class P-homeomorphisms to diffeomorphisms

Abdelhamid Adouani·Habib Marzougui
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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 piecewise C^1 and even more it is not absolutely continuous function if the total product of f-jumps in all the break points is non-trivial.

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Abdelhamid Adouani, Habib Marzougui. 2015-08-14. A sharp smoothness of the conjugation of class P-homeomorphisms to diffeomorphisms. https://arxiv.org/abs/1508.03549

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