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Bifurcations in Hamiltonian Systems Computing Singularities by Gröbner Bases

The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part al...

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Bibliographic Details
Main Authors: Broer, Henk, Hoveijn, Igor (Author), Lunter, Gerton (Author), Vegter, Gert (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2003, 2003
Edition:1st ed. 2003
Series:Lecture Notes in Mathematics
Subjects:
Global Analysis And Analysis On Manifolds
Computational Science And Engineering
Computer Mathematics
Manifolds (mathematics)
Global Analysis (mathematics)
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Introduction
  • I. Applications: Methods I: Planar reduction; Method II: The energy-momentum map
  • II. Theory: Birkhoff Normalization; Singularity Theory; Gröbner bases and Standard bases; Computing normalizing transformations
  • Appendix A.1. Classification of term orders; Appendix A.2. Proof of Proposition 5.8
  • References
  • Index

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