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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Veröffentlicht in:Mathematics in computer science Jg. 18; H. 4
Hauptverfasser: Batkhin, Alexander, Khaydarov, Zafar
Format: Journal Article
Sprache:Englisch
Veröffentlicht: 01.12.2024
ISSN:1661-8270, 1661-8289
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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