q-Nonlinearity, Deformations and Planck Distribution

In this contribution we will review a new approach to some nonlinear dynamical systems which is related to the q-deformation (or other types of deformations) of linear classical and quantum systems considered in [1]. The main idea of this approach is to replace constants like frequency or mass, etc., which are parameters of the linear systems with constants of the motion of the system. This procedure produces from the initial linear system a nonlinear one and as it was demonstrated in [1], [2] the q-oscillator of [3], [4] may be considered as a physical system with a specific nonlinearity which was called q-nonlinearity. In the example of the q-oscillator the constant parameter which was replaced by the constant of the motiom was the frequency, which became dependent on the amplitude of the vibration.