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Nonlinear Oscillations

, 12:244 | Cite as

Dynamics of a quantized circle homeomorphism with quasiperiodic perturbation

  • O. Yu. Teplins’kyi
Article
  • 23 Downloads

We introduce the notion of a quantized circle homeomorphism that is a discontinuous mapping of an interval shift, which is widely used in modern digital radio electronics. For a two-dimensional dynamical system given by a triangular mapping, which is a quantized circle homeomorphism with quasiperiodic perturbation, we prove, under some assumptions, that there exist an invariant absorbing belt and a repulsive contour, study properties of these structures, and get estimates for their sizes. To make the exposition complete, we, first, study the corresponding problems for three less complicated systems, namely, a proper circle homeomorphism, a proper circle homeomorphism with quasiperiodic perturbation, and a quantized circle homeomorphism without perturbation.

Keywords

Triangular Mapping Uniform Quantizer Mode Capture Half Interval Circle Homeomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • O. Yu. Teplins’kyi
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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