Normalization of a periodic Hamiltonian system

DOI10.1134/S0361768820020048zbMath1459.37048OpenAlexW3017145192MaRDI QIDQ2217193

Alexander D. Bruno

Publication date: 18 December 2020

Published in: Programming and Computer Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0361768820020048

zbMATH Keywords

fixed pointsnormal formsautonomous Hamiltonian system

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Hamilton's equations (70H05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (9)

Five new methods of celestial mechanics ⋮ Low dimensional completely resonant tori in Hamiltonian lattices and a theorem of Poincaré ⋮ Boundaries of the region of stability of autonomous Hamiltonian systems ⋮ On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori ⋮ Integrals of motion in time-periodic Hamiltonian systems: the case of the Mathieu equation ⋮ Invariant coordinate subspaces of normal form of a system of ordinary differential equations ⋮ Continuation of spatially localized periodic solutions in discrete NLS lattices via normal forms ⋮ Order and chaos in time periodic Hamiltonian systems ⋮ Stability of equilibrium points for a Hamiltonian systems with two degrees of freedom in the problem of parametric resonance

Uses Software

• Maple
• Mathematica
• SymPy
• MathPartner

Cites Work

• Unique normal forms: The nilpotent Hamiltonian case
• MathPartner computer algebra
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