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Abstract and Applied Analysis
Volume 2014, Article ID 378742, 6 pages
http://dx.doi.org/10.1155/2014/378742
Research Article

On Critical Circle Homeomorphisms with Infinite Number of Break Points

1Turin Polytechnic University, Kichik Halka Yuli 17, 100095 Tashkent, Uzbekistan
2School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor Darul Ehsan, Malaysia

Received 4 October 2013; Accepted 30 January 2014; Published 20 March 2014

Academic Editor: Weinian Zhang

Copyright © 2014 Akhtam Dzhalilov et al. 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

We prove that a critical circle homeomorphism with infinite number of break points without periodic orbits is conjugated to the linear rotation by a quasisymmetric map if and only if its rotation number is of bounded type. And we also prove that any two adjacent atoms of dynamical partition of a unit circle are comparable.