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2014•Abstract and Applied AnalysisOpen access

On Critical Circle Homeomorphisms with Infinite Number of Break Points

Akhtam Abdurakhmanovich Dzhalilov, Mohd Salmi Md Noorani, Sokhobiddin Akhatkulov

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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.

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What this paper is about

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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Available 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.

Key concepts: Rotation number, Unit circle, Mathematics, Homeomorphism (graph theory), Bounded function, Partition (number theory), Rotation (mathematics), Great circle

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