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Bifurcations and Periodic Orbits of Vector Fields

  • Dana Schlomiuk

Part of the NATO ASI Series book series (ASIC, volume 408)

About this book

Introduction

The last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "Bifurcations and periodic orbits of vector fields". This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy­ namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work.

Keywords

computer computer algebra differential equation dynamical systems perturbation perturbation theory

Editors and affiliations

  • Dana Schlomiuk
    • 1
  1. 1.Département de mathématiques et de statistiqueUniversité de MontréalMontréalCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8238-4
  • Copyright Information Springer Science+Business Media B.V. 1993
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4303-0
  • Online ISBN 978-94-015-8238-4
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site