|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910144633903321 |
|
|
Autore |
Broer Henk |
|
|
Titolo |
Bifurcations in Hamiltonian Systems : Computing Singularities by Gröbner Bases / / by Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2003 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[1st ed. 2003.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (XVI, 172 p.) |
|
|
|
|
|
|
Collana |
|
Lecture Notes in Mathematics, , 0075-8434 ; ; 1806 |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Global analysis (Mathematics) |
Manifolds (Mathematics) |
Computer mathematics |
Global Analysis and Analysis on Manifolds |
Computational Science and Engineering |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Bibliographic Level Mode of Issuance: Monograph |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references (pages [159]-165) and index. |
|
|
|
|
|
|
Nota di contenuto |
|
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. |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
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 allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced |
|
|
|
|