Nonlinear Oscillations

, 12:244 | Cite as

Dynamics of a quantized circle homeomorphism with quasiperiodic perturbation

  • O. Yu. Teplins’kyi

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.


Triangular Mapping Uniform Quantizer Mode Capture Half Interval Circle Homeomorphism 
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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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