On Critical Circle Homeomorphisms with Infinite Number of Break Points

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 uni...

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Main Authors: Akhtam Dzhalilov, Mohd Salmi Md Noorani, Sokhobiddin Akhatkulov
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/378742
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author Akhtam Dzhalilov
Mohd Salmi Md Noorani
Sokhobiddin Akhatkulov
author_facet Akhtam Dzhalilov
Mohd Salmi Md Noorani
Sokhobiddin Akhatkulov
author_sort Akhtam Dzhalilov
collection DOAJ
description 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.
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institution DOAJ
issn 1085-3375
1687-0409
language English
publishDate 2014-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-42ba32c49865403fbb327e7fd03d334b2025-08-20T02:39:16ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/378742378742On Critical Circle Homeomorphisms with Infinite Number of Break PointsAkhtam Dzhalilov0Mohd Salmi Md Noorani1Sokhobiddin Akhatkulov2Turin Polytechnic University, Kichik Halka Yuli 17, 100095 Tashkent, UzbekistanSchool of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor Darul Ehsan, MalaysiaSchool of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor Darul Ehsan, MalaysiaWe 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.http://dx.doi.org/10.1155/2014/378742
spellingShingle Akhtam Dzhalilov
Mohd Salmi Md Noorani
Sokhobiddin Akhatkulov
On Critical Circle Homeomorphisms with Infinite Number of Break Points
Abstract and Applied Analysis
title On Critical Circle Homeomorphisms with Infinite Number of Break Points
title_full On Critical Circle Homeomorphisms with Infinite Number of Break Points
title_fullStr On Critical Circle Homeomorphisms with Infinite Number of Break Points
title_full_unstemmed On Critical Circle Homeomorphisms with Infinite Number of Break Points
title_short On Critical Circle Homeomorphisms with Infinite Number of Break Points
title_sort on critical circle homeomorphisms with infinite number of break points
url http://dx.doi.org/10.1155/2014/378742
work_keys_str_mv AT akhtamdzhalilov oncriticalcirclehomeomorphismswithinfinitenumberofbreakpoints
AT mohdsalmimdnoorani oncriticalcirclehomeomorphismswithinfinitenumberofbreakpoints
AT sokhobiddinakhatkulov oncriticalcirclehomeomorphismswithinfinitenumberofbreakpoints