Asymptotic approaches in nonlinear dynamics. New trends and applications
type: Item
instance of: scholarly article
title: Asymptotic approaches in nonlinear dynamics. New trends and applications
zbMATH Open document ID: 0910.70001
author: K. Appert
published in: Springer Series in Synergetics
publication date: 1998-11-04T00:00:00Z
review text: This book gives an introduction into the field of asymptotic simplification of problems of the theory of oscillations. On the other hand there is no lack in good books treating the application of asymptotic methods to problems of nonlinear mechanics. Hence quite naturally the question arises: what specific aspects justify the publication of a new book? A positive answer in the present case is quite obvious because the great asset of this book is that two of the authors are from countries (Russia, Ukraine) where the asymptotic theories for the treatment of nonlinear oscillations have been mostly developed during the past century and are still treated nowadays on a very high level. However, a great part of the corresponding literature is still published in the native language of these countries and hence not easily accessible. In this book, many results are reported in English language for the first time in a unified and pedagogically well-done way. The content of the book covers the basic principles of asymptotics and deals on the one hand with traditional approaches, such as regular and singular perturbations, averaging and homogenization. On the other hand, the authors present some less well-known approaches like Padé approximants, the distributional approach and the method of boundary perturbations. Pedagogically, it is very appealing that almost all concepts are introduced and explained by means of well selected examples from nonlinear mechanics which are easy to understand and which partly are worked out in a very detailed manner. This book can be highly recommended to every scientist working in the field of asymptotic methods in nonlinear dynamics.
Mathematics Subject Classification ID: 70-02
Mathematics Subject Classification ID: 70K99
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 1219760
zbMATH Keywords: regular perturbations
zbMATH Keywords: singular perturbations
zbMATH Keywords: averaging
zbMATH Keywords: homogenization
zbMATH Keywords: Padé approximants
zbMATH Keywords: distributional approach
zbMATH Keywords: method of boundary perturbations
reviewed by: Hans Troger
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1219760