Introduction

Abstract

Asymptotic methods of nonlinear mechanics developed by N.M. Krylov and N.N. Bogoliubov originated new trend in perturbation theory. They penetrated deep into various applied branches (theoretical physics, mechanics, applied astronomy, dynamics of space flights, and others) and laid the foundation for numerous generalizations and for the creation of various modifications of these methods. A great number of approaches and techniques exist and many different classes of mathematical objects have been considered (ordinary differential equations, partial differential equations, delay differential equations and others).