Abstract
Let \(f_{1}\) and \(f_{1}\) be orientation preserving circle homeomorphisms with single critical point of non-integer order and same irrational rotation numbers. We prove that if the orders of critical points are different then the map h conjugating \(f_1\) and \(f_2\) is a singular function.
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Acknowledgements
The author would like to thank Professors A. A. Dzhalilov and K. M. Khanin for making several useful suggestions which improved the text of the paper.
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Safarov, U. (2018). Conjugations Between Two Critical Circle Maps With Non-integer Exponents. In: Azamov, A., Bunimovich, L., Dzhalilov, A., Zhang, HK. (eds) Differential Equations and Dynamical Systems. USUZCAMP 2017. Springer Proceedings in Mathematics & Statistics, vol 268. Springer, Cham. https://doi.org/10.1007/978-3-030-01476-6_12
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DOI: https://doi.org/10.1007/978-3-030-01476-6_12
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