TY - JOUR AU - Akhatkulov, Sokhobiddin AU - Noorani, Mohd. Salmi Md. AU - Akhadkulov, Habibulla PY - 2017 TI - On the invariant measure of a piecewise-smooth circle homeomorphism of Zygmund class JO - Journal of Nonlinear Sciences and Applications SP - 48--59 VL - 10 IS - 1 AB - We prove that the invariant probability measure of an orientation preserving circle homeomorphism f with several break points (at which the derivative \(\acute{f}\) has jumps) is singular with respect to Lebesgue measure, if \(\acute{f}\) satisfies certain condition and the product of jump ratios at break points is non-trivial. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.01.05 DO - 10.22436/jnsa.010.01.05 ID - Akhatkulov2017 ER -