A symbolic approximation of periodic solutions of the Henon--Heiles system by the normal form method

DOI10.1016/S0378-4754(97)00122-5zbMath1017.34501MaRDI QIDQ1404731

Victor F. Edneral

Publication date: 21 August 2003

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

zbMATH Keywords

Dynamical systemsComputer algebraHenon-Heiles systemResonant normal form

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Periodic solutions to ordinary differential equations (34C25) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (7)

POINCARé CODE: a package of open-source implements for normalization and computer algebra reduction near equilibria of coupled ordinary differential equations ⋮ Asymptotic solution of the Hénon-Heiles Hamiltonian system ⋮ Normal forms and integrability of ODE systems ⋮ Some qualitative properties of Lyapunov exponents for almost periodic Hamiltonian systems ⋮ Parallelization of perturbation analysis: Application to large-scale engineering problems ⋮ Normal form methods for symbolic creation of approximate solutions of nonlinear dynamical systems ⋮ Nonlinear oscillations of a spring pendulum at the 1:1:2 resonance by normal form methods

Uses Software

• REDUCE

Cites Work

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• Bifurcations of solutions in an invertible system of ordinary differential equations
• Package for reducing ordinary differential equations to normal form

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