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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| Autors principals: | , , , |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Col·lecció: | Lecture notes in mathematics
1806 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Bifurcations in Hamiltonian systems, computing singularities by Gröbner bases, Henk Broer, Igor Hoveijn, Gerton Lunter ... [et al.], 2003, Berlin, Springer, 1 vol. (XIII-169 p.), Lecture notes in mathematics, 978-3-540-00403-5 • Bifurcations in Hamiltonian Systems, Texte imprimé, 9783662193358 |
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| 100 | 1 | |a Broer, Hendrik Wolter, |d 1950-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Bifurcations in Hamiltonian Systems : |b Computing Singularities by Gröbner Bases |c Henk Broer, Igor Hoveijn, Gerton Lunter, Gert Vegter. |
| 260 | |a Berlin [etc.] : |b Springer. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Lecture notes in mathematics |v 1806 |x 1617-9692 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 graduate students and researchers in dynamical systems. | ||
| 650 | |a Singularités (mathématiques) | ||
| 650 | |a Bases de Gröbner | ||
| 650 | |a Systèmes hamiltoniens | ||
| 650 | |a Théorie de la bifurcation | ||
| 650 | |a Mathématiques | ||
| 650 | |a Informatique |x Mathématiques | ||
| 650 | |a Analyse globale (mathématiques) | ||
| 700 | 1 | |a Hoveijn, Igor, |d 19..- |4 aut | |
| 700 | 1 | |a Vegter, Gert, |c mathématicien. |4 aut | |
| 700 | 1 | |a Lunter, Gerton, |d 19..- |4 aut | |
| 776 | 0 | |0 077094220 |t Bifurcations in Hamiltonian systems |o computing singularities by Gröbner bases |f Henk Broer, Igor Hoveijn, Gerton Lunter ... [et al.] |d 2003 |c Berlin |n Springer |p 1 vol. (XIII-169 p.) |s Lecture notes in mathematics |z 978-3-540-00403-5 | |
| 776 | 0 | |t Bifurcations in Hamiltonian Systems |b Texte imprimé |z 9783662193358 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/b10414 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-V8VS5TCP-V |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:750652950 |u https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.1007/b10414 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:754003175 |u https://ezproxy.insa-cvl.fr/login?qurl=https://doi.org/10.1007/b10414 |z Accès INSA CVL | |
| 997 | |0 971402 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||