Geodesic
On the invariant measure of a piecewise-smooth circle homeomorphism of Zygmund class
Akhatkulov, Sokhobiddin1 ; Noorani, Mohd. Salmi Md.1 ; Akhadkulov, Habibulla2
1 School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia
2 School of Quantitative Sciences, University Utara Malaysia, CAS 06010, UUM Sintok, Kedah DA, Malaysia
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 48-59.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.01.05
Classification : 37E10, 37C15, 26D99
Keywords: Break point, circle homeomorphism, invariant measure, rotation number.

Akhatkulov, Sokhobiddin 1 ; Noorani, Mohd. Salmi Md. 1 ; Akhadkulov, Habibulla 2

1 School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia
2 School of Quantitative Sciences, University Utara Malaysia, CAS 06010, UUM Sintok, Kedah DA, Malaysia 
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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 its applications, Tome 10 (2017) no. 1, p. 48-59. doi : 10.22436/jnsa.010.01.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.01.05/

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