On Critical Circle Homeomorphisms with Infinite Number of Break Points

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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Veröffentlicht in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.212-217-525
Hauptverfasser: Dzhalilov, Akhtam, Akhatkulov, Sokhobiddin, Noorani, Mohd Salmi Md
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Breaking
Homeomorphisms
Mathematical problems
Orbits
Partitions
Power plants
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Zusammenfassung: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/378742