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On Critical Circle Homeomorphisms with Infinite Number of Break Points

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  • Akhtam Dzhalilov
  • Mohd Salmi Md Noorani
  • Sokhobiddin Akhatkulov

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.

Suggested Citation

  • Akhtam Dzhalilov & Mohd Salmi Md Noorani & Sokhobiddin Akhatkulov, 2014. "On Critical Circle Homeomorphisms with Infinite Number of Break Points," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, March.
    • Handle: RePEc:hin:jnlaaa:378742
    DOI: 10.1155/2014/378742
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