Rotation number quantization effect

V. M. Buchstaber, O. V. Karpov, S. I. Tertychniy

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We study a class of dynamical systems on a torus that includes dynamical systems modeling the dynamics of the Josephson transition. For systems in this class, we introduce certain characteristics including a sequence of functions depending on the system parameters. We prove that if this sequence converges at a given point in the parameter space, then its limit is equal to the classical rotation number, and we then call this point a quantization point for the rotation number. We prove that the rotation number of such a system takes only integer values at a quantization point. Quantization areas are thus defined in the parameter space, and the problem of effectively describing them becomes an important part of characterizing the systems under study. We present graphs of the rotation number at quantization points and under conditions when it is not quantized (an example of a half-integer rotation number) and diagrams for quantization areas.

Original languageEnglish
Pages (from-to)211-221
Number of pages11
JournalTheoretical and Mathematical Physics
Issue number2
Publication statusPublished - 2010
Externally publishedYes


  • Dynamical system on a torus
  • Josephson effect
  • Quantization
  • Rotation number


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