Bifurcations in Hamiltonian Systems Computing Singularities by Gröbner Bases /

• Main Authors: Broer, Henk (Author, http://id.loc.gov/vocabulary/relators/aut), Hoveijn, Igor (http://id.loc.gov/vocabulary/relators/aut), Lunter, Gerton (http://id.loc.gov/vocabulary/relators/aut), Vegter, Gert (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Edition: 1st ed. 2003.
• Series: Lecture Notes in Mathematics, 1806
• Subjects: Global analysis (Mathematics).; Manifolds (Mathematics).; Computer mathematics.; Global Analysis and Analysis on Manifolds.; Computational Science and Engineering.

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...

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.