A note on the conjugacy between two critical circle maps

Utkir A. Safarov<sup>ab

a</sup> Turin Politechnic University in Tashkent, Tashkent, Uzbekistan
^b Tashkent State University of Economics,Tashkent, Uzbekistan

Abstract: We study a conjugacy between two critical circle homeomorphisms with irrational rotation number. Let $f_{i}, i=1,2$ be a $C^{3}$ circle homeomorphisms with critical point $x_{cr}^{(i)}$ of the order $2m_{i}+1$. We prove that if $2m_{1}+1 \neq 2m_{2}+1$, then conjugating between $f_{1}$ and $f_{2}$ is a singular function.

Keywords: circle homeomorphism, critical point, conjugating map, rotation number, singular function.

UDC: 517.9+519.1

Received: 10.11.2020
Received in revised form: 16.12.2020
Accepted: 04.02.2021

Language: English

DOI: 10.17516/1997-1397-2021-14-3-287-300

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