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Symmetry and Perturbation Theory in Nonlinear Dynamics

  • Book
  • © 1999

Overview

Authors:
  1. Giampaolo Cicogna

    1. Dipartimento di Fisica, Università di Pisa, Pisa, Italy

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  2. Giuseppe Gaeta

    1. Dipartimento di Fisica, Università di Roma, Roma, Italy
      Depto de Matematicas, Universidad Carlos III de Madrid, Leganes, Spain

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction

    Pages 1-18

  3. Symmetry and Differential Equations

    Pages 19-40

  4. Dynamical Systems

    Pages 41-66

  5. Symmetries of Dynamical Systems

    Pages 67-82

  6. Normal Forms and Symmetries for Dynamical Systems

    Pages 83-114

  7. Normal Forms and Symmetries for Hamiltonian Systems

    Pages 115-134

  8. Convergence of the Normalizing Transformations

    Pages 135-150

  9. Invariant Manifolds

    Pages 151-161

  10. Further Normalization

    Pages 163-182

  11. Asymptotic Symmetries

    Pages 183-192

  12. Back Matter

    Pages 193-208
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Keywords

About this book

has been in the of a Symmetry major ingredient development quantum perturba tion and it is a basic of the of theory, ingredient theory integrable (Hamiltonian and of the the use in context of non Hamiltonian) systems; yet, symmetry gen eral is rather recent. From the of view of nonlinear perturbation theory point the use of has become dynamics, widespread only through equivariant symmetry bifurcation in this attention has been confined to linear even theory; case, mostly symmetries. in recent the and of methods for dif Also, theory practice symmetry years ferential has become and has been to a equations increasingly popular applied of the of the book Olver This by variety problems (following appearance [2621). with is and deals of nature theory deeply geometrical symmetries general (pro vided that described i.e. in this context there is are vector no they by fields), to limit attention to linear reason symmetries. In this look the basic tools of i.e. normal book we at perturbation theory, introduced Poincar6 about and their inter a forms (first by century ago) study action with with no limitation to linear ones. We focus on the most symmetries, basic fixed the and i.e. a setting, systems having point (at origin) perturbative around thus is local.

Authors and Affiliations

  • Dipartimento di Fisica, Università di Pisa, Pisa, Italy

    Giampaolo Cicogna

  • Dipartimento di Fisica, Università di Roma, Roma, Italy

    Giuseppe Gaeta

  • Depto de Matematicas, Universidad Carlos III de Madrid, Leganes, Spain

    Giuseppe Gaeta

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