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Quasi-symmetric conjugacy for circle maps with a flat interval

Published online by Cambridge University Press:  20 June 2017

LIVIANA PALMISANO
LIVIANA PALMISANO*
Affiliation:
IMPAN, ul. Śniadeckich 8, 00-656 Warszawa, Poland email l.palmisano@impan.pl
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Abstract

In this paper we study quasi-symmetric conjugations of ${\mathcal{C}}^{2}$ weakly order-preserving circle maps with a flat interval. Under the assumption that the maps have the same rotation number of bounded type and that bounded geometry holds, we construct a quasi-symmetric conjugation between their non-wandering sets. Further, this conjugation is extended to a quasi-symmetric circle homeomorphism. Our proof techniques hinge on real-dynamic methods, allowing us to construct the conjugation under general and natural assumptions.

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Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 2 , February 2019 , pp. 425 - 445
Copyright
© Cambridge University Press, 2017 

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