Asymptotic approaches in mechanics: New parameters and procedures

Abstract

This survey is devoted to recent achievements in the field of asymptotic approaches. Here we consider the asymptotics in relation to completely new and sometimes unexpected parameters. Some procedures leading to improvement and isolation of the essential analytical structure of the perturbation series are presented. It is also shown that many problems of perturbation theory, which seem to be relatively simple at a first glance, are still far from completely solved. Different asymptotic techniques to solve the same problem and their influence on the results are briefly illustrated and discussed. This review paper contains 310 references.