On the invariant measure of a piecewise-smooth circle homeomorphism of Zygmund class
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Authors
Sokhobiddin Akhatkulov
- School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia.
Mohd. Salmi Md. Noorani
- School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia.
Habibulla Akhadkulov
- School of Quantitative Sciences, University Utara Malaysia, CAS 06010, UUM Sintok, Kedah DA, Malaysia.
Abstract
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.
Share and Cite
ISRP Style
Sokhobiddin Akhatkulov, Mohd. Salmi Md. Noorani, Habibulla Akhadkulov, On the invariant measure of a piecewise-smooth circle homeomorphism of Zygmund class, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 1, 48--59
AMA Style
Akhatkulov Sokhobiddin, Noorani Mohd. Salmi Md., Akhadkulov Habibulla, On the invariant measure of a piecewise-smooth circle homeomorphism of Zygmund class. J. Nonlinear Sci. Appl. (2017); 10(1):48--59
Chicago/Turabian Style
Akhatkulov, Sokhobiddin, Noorani, Mohd. Salmi Md., Akhadkulov, Habibulla. "On the invariant measure of a piecewise-smooth circle homeomorphism of Zygmund class." Journal of Nonlinear Sciences and Applications, 10, no. 1 (2017): 48--59
Keywords
- Break point
- circle homeomorphism
- invariant measure
- rotation number.
MSC
References
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