Work

Resonances and Formal Stability Investigation in Hamiltonian Systems

Year: 2024

Type: article

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.

Source: Mathematics in Computer Science

DOI: 10.1007/s11786-024-00596-9

Authors: Alexander Batkhin, Zafar Khaydarov

Institutions: Technion – Israel Institute of Technology, Keldysh Institute of Applied Mathematics, Samarkand State University named after Sharof Rashidov

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Technion-Israel Institute of Technology