A Decomposition of Quasi-Oscillators

Shahverdian, Ashot

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A Decomposition of Quasi-Oscillators

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Shahverdian, Ashot
Max Planck Research Group Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Shahverdian, A. (2009). A Decomposition of Quasi-Oscillators. 4, 681-705.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-12B1-D

Abstract

A decomposition of a simplest mechanical system { a q-oscillator, is considered. A q- oscillator (quasi-oscillator) is de ned as a system consisting of a particle moving on a linear segment with a constant speed and re ecting from the segment's end-points. A theorem, stating that a discrete-time version of q-oscillator can be decomposed into a countable set of discrete-time rotators (a rotator consists of a particle rotating on a circle with a constant angular rate) as well as a metrical theorem, concerning the rate of such decomposition, are proved. Some physics-related examples are discussed. A phase-shifting perturbed rotator and a number-theoretical matrix system modelling the quantum oscillator, are presented.