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A circle diffeomorphism with breaks that is absolutely continuously linearizable

Published online by Cambridge University Press:  04 July 2016

ALEXEY TEPLINSKY
ALEXEY TEPLINSKY*
Affiliation:
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska Street, Kiev 01601, Ukraine email teplinsky@imath.kiev.ua, teplinsky.a@gmail.com
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 1 , February 2018 , pp. 371 - 383
Copyright
© Cambridge University Press, 2016 

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