Resonances and Formal Stability Investigation in Hamiltonian Systems
This paper proposes a method for studying formal stability of equilibrium points in multiparameter Hamiltonian systems with three degrees of freedom. We detail a technique for the symbolic computation of resonance conditions, employing computer algebra and power geometry to represent the resonant va...
Gespeichert in:
| Veröffentlicht in: | Mathematics in computer science Jg. 18; H. 4 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
01.12.2024
|
| ISSN: | 1661-8270, 1661-8289 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | This paper proposes a method for studying formal stability of equilibrium points in multiparameter Hamiltonian systems with three degrees of freedom. We detail a technique for the symbolic computation of resonance conditions, employing computer algebra and power geometry to represent the resonant variety as a rational algebraic curve and provide its polynomial parametrization. A non-trivial example of formal stability investigation is considered. An implementation of resonant variety calculations in the computer algebra system Maple is also discussed. |
|---|---|
| ISSN: | 1661-8270 1661-8289 |
| DOI: | 10.1007/s11786-024-00596-9 |