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
Main Authors: Batkhin, Alexander, Khaydarov, Zafar
Format: Journal Article
Language:English
Published: 01.12.2024
ISSN:1661-8270, 1661-8289
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Abstract 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.
AbstractList 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.
ArticleNumber 22
Author Khaydarov, Zafar
Batkhin, Alexander
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