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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 134701, 12 pages
http://dx.doi.org/10.1155/2012/134701
Research Article

On Absolute Continuity of Conjugations between Circle Maps with Break Points

1School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, Bangi, 43600 Selangor, Malaysia
2Faculty of Mathematics and Mechanics, Samarkand State University, Boulevard Street 15, 703004 Samarkand, Uzbekistan

Received 31 August 2012; Accepted 23 October 2012

Academic Editor: Ivanka Stamova

Copyright © 2012 Habibulla Akhadkulov and Mohd Salmi Md Noorani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let and be piecewise smooth circle homeomorphisms with break points and identical irrational rotation numbers. We provide one sufficient and necessary condition for the absolute continuity of conjugation map between and .