# American Institute of Mathematical Sciences

November  2021, 41(11): 5037-5055. doi: 10.3934/dcds.2021067

## A phase transition for circle maps with a flat spot and different critical exponents

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* Corresponding author: Liviana Palmisano

Received  July 2019 Revised  January 2021 Published  November 2021 Early access  April 2021

Fund Project: The authors would like to thank the referees whose valuable comments helped to improve the exposition of the paper. The first author is supported by the Trygger Foundation. The second author is supported by the Centre d'Excellence Africain en Science Mathématiques et Applications (CEA-SMA). Part of the research for this paper took place at ICTP. The authors would like to thank the ICTP and in particular Prof. Stefano Luzzatto for their hospitality and support

We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the critical exponents. At this boundary there is a phase transition in the geometry of the system. Differently from the previous approaches, this is achieved by studying the asymptotical behavior of the renormalization operator.

Citation: Liviana Palmisano, Bertuel Tangue Ndawa. A phase transition for circle maps with a flat spot and different critical exponents. Discrete & Continuous Dynamical Systems, 2021, 41 (11) : 5037-5055. doi: 10.3934/dcds.2021067
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##### References:
A function in $\mathscr{ L}^{(X)}$
The curve $\Gamma$. The quadrant $Q_-$ is below $\Gamma$ and the quadrant $Q_+$ is above $\Gamma$
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