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...
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| Published in: | Mathematics in computer science Vol. 18; no. 4 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.12.2024
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| ISSN: | 1661-8270, 1661-8289 |
| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 1661-8270 1661-8289 |
| DOI: | 10.1007/s11786-024-00596-9 |