Dynamics of a quantized circle homeomorphism with quasiperiodic perturbation
- 22 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.
KeywordsTriangular Mapping Uniform Quantizer Mode Capture Half Interval Circle Homeomorphism
- 1.O. Yu. Teplins’kyi, “Mapping of a shift of intervals as a unified approach to the study of the dynamics of a series of models of discretized electronic devices,” Dopov. Nats. Akad. Nauk Ukr., No. 12, 40–45 (2008).Google Scholar
- 3.O. Yu. Teplins’kyi, “Limiting absorbing belt for a quasiperiodically driven mapping of the shift of intervals,” Ukr. Mat. Zh., 61, No. 3, 408–417 (2009).Google Scholar
- 6.A. N. Sharkovskii, S. F. Kolyada, A. G. Sivak, and V. V. Fedorenko, Dynamics of One-Dimensional Mappings [in Russian], Naukova Dumka, Kiev (1989).Google Scholar