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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/378742 |
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| _version_ | 1850104726297772032 |
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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. |
| format | Article |
| id | doaj-art-42ba32c49865403fbb327e7fd03d334b |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |