Let f be a circle homeomorphism with single critical point of non-integer order, that is, 1()()||()dcrcrcrfxxxxxfx−=−−+, 2d>, for some δ-neighborhood ()crUxδ. We prove that, if the homeomorphism f is P-homeomorphism on the set 1\()crSUxδ with irrational rotation numberfρ, then f is topologically conjugate to the pure rotation fρ . Moreover, ϕ is quasi-symmetric if and only if fρ is of bounded type.
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"Quasi-Symmetric Distribution Function of Invariant Measure of Circle Homeomorphisms with Singularities,"
Acta of Turin Polytechnic University in Tashkent: Vol. 8
, Article 1.
Available at: https://uzjournals.edu.uz/actattpu/vol8/iss2/1