Perturbation theory free from secular terms for the equations of motion ofanharmonic oscillators

We develop a time-independent perturbation theory in operator form for the equations of motion of classical and quantum-mechanical anharmonic oscillat ors. The method focuses on the frequency of the motion in the former case a nd in a frequency operator in the latter, producing a power series in a sma ll coupling constant. The resulting expressions are free from secular insta bilities that commonly appear in perturbation treatments of nonlinear probl ems. (C) 2001 American Institute of Physics.