ADIABATIC INVARIANTS OF QUASI-PURE-CUBIC OSCILLATORS

The adiabatic invariants for quasi-pure-cubic oscillators with slowly varying parameters are obtained. The method developed for dynamic syst ems with small non-linearities [1] is extended to systems with large n on-linearity. The method is based on Noether's theorem for invariance and the elliptic Krylov-Bogoliubov method. A set of adiabatic invarian ts is applied to find the asymptotic solution for the motion. Two exam ples are considered: the pure cubic oscillator and the linear damped q uasi-pure-cubic oscillator with variable mass.