Long Time Stability in Perturbations of Completely Resonant PDE's

摘要: In this paper we will present some results concerning long time stability in nonlinear perturbations of resonant linear PDE's with discrete spectrum. particular prove that if the perturbation satisfies a suitable nondegeneracy condition then there exists periodic like trajectory, i.e. closed curve phase space property solutions starting close to it remain for very times. Secondly, special case where average main part is integrable energy initially essentially concentrated on finitely many modes, along corresponding all actions are approximatively constant Applications wave and Schrodinger equations segment also be given.