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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