On the study of a system close to a harmonic oscillator via approximate point mapping

The theory of nonlinear oscillations is one of the most important components of modern science. Nonlinear oscillation is a term usually applied to oscillatory phenomena that occur in nonlinear dynamical systems. The most accessible for research are oscillatory systems with low nonlinearity, for which various asymptotic methods have been developed. Moreover, the study of nonlinear systems close to a harmonic oscillator is still of particular interest. The current study assesses the possibility of studying a system close to harmonic oscillators by via approximate point mapping, both equations of which contain nonlinear terms. The article provides explicitly defined functions of the sequence of a point map, in the construction of which asymptotic methods are used, as well as the results of their analysis.