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3. Method II: The energy-momentum map

  • Henk Broer
  • Igor Hoveijn
  • Gerton Lunter
  • Gert Vegter
I Applications
Part of the Lecture Notes in Mathematics book series (LNM, volume 1806)

Abstract

  • 3.1 Introduction

  • 3.2 Description of the method
    • 3.2.1 Birkhoff normalization

    • 3.2.2 Circle-equivariant vector fields

    • 3.2.3 The energy-momentum map

    • 3.2.4 Removing the \(\chi \)-dependence

  • 3.3 Application to several resonances
    • 3.3.1 The 1:2 resonance

    • 3.3.2 The 1:3 resonance

    • 3.3.3 The 1:4 resonance

  • 3.4 Spring-pendulum in 1:2 resonance
    • 3.4.1 Bifurcation analysis of the 1:2-resonant normal form

    • 3.4.2 Pictures

    • 3.4.3 Inducing the system from the model

Mathematics Subject Classification (2000):

58C27 58F14 58F36 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • Henk Broer
    • 1
  • Igor Hoveijn
    • 1
  • Gerton Lunter
    • 2
  • Gert Vegter
    • 1
  1. 1.Department of Mathematics and Computing SciencesUniversity of GroningenGroningenThe Netherlands
  2. 2.Department of StatisticsOxford UniversityOxfordUnited Kingdom

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