A circle diffeomorphism with breaks that is absolutely continuously linearizable

In this paper we answer positively to a question of whether it is possible for a circle diffeomorphism with breaks to be smoothly conjugate to a rigid rotation in the case where its breaks are lying on pairwise distinct trajectories. An example constructed is a piecewise linear circle homeomorphism that has four break points lying on distinct trajectories and whose invariant measure is absolutely continuous with respect to the Lebesgue measure. The irrational rotation number for our example can be chosen to be a Roth number, but not of bounded type.

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