Resumen de A Specialized Multiphase Averaging Method for Quasiperiodic Systems of ODEs

H. Scott Dumas

• We present a specialized averaging method for systems of ordinary differential equations whose fast variables evolve quasiperiodically. We include results for both nonresonant and resonant normal forms, and results on adiabatic invariance for systems with vanishing average. In our method, nonresonance conditions on the frequencies are weak and easily verified, and they give precise meaning to the notion that “resonances above a certain order may be ignored.” Moreover, the normal forms have nice dependence on the frequencies, and the proofs are especially simple, involving no coordinate transformations and instead using a new generalized form of the “Besjes inequality.”