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Symmetry and Perturbation Theory in Nonlinear Dynamics

  • Giampaolo Cicogna
  • Giuseppe Gaeta

Part of the Lecture Notes in Physics book series (LNPMGR, volume 57)

Table of contents

About this book

Introduction

This book deals with the theory of Poincaré--Birkhoff normal forms, studying symmetric systems in particular. Attention is focused on general Lie point symmetries, and not just on symmetries acting linearly. Some results on the simultaneous normalization of a vector field describing a dynamical system and vector fields describing its symmetry are presented and a perturbative approach is also used. Attention is given to the problem of convergence of the normalizing transformation in the presence of symmetry, with some other extensions of the theory. The results are discussed for the general case of dynamical systems and also for the specific Hamiltonian setting.

Keywords

Dynamical system dynamical systems nonlinear dynamics nonlinear systems normal forms symmetries

Authors and affiliations

  • Giampaolo Cicogna
    • 1
  • Giuseppe Gaeta
    • 2
    • 3
  1. 1.Dipartimento di FisicaUniversità di PisaPisaItaly
  2. 2.Dipartimento di FisicaUniversità di RomaRomaItaly
  3. 3.Depto de MatematicasUniversidad Carlos III de MadridLeganesSpain

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-48874-X
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-65904-4
  • Online ISBN 978-3-540-48874-3
  • Series Print ISSN 0940-7677
  • Buy this book on publisher's site