A Decomposition of a Quasi-oscillator

A decomposition of a simplest mechanical system – a q-oscillator, is considered. A qoscillator (quasi-oscillator) is defined as a system consisting of a particle moving on a linear segment with a constant speed and reflecting 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.