Symbolic computation of a homological equation of an arbitrary order and reduction of Hamiltonian system to its normal form

DOI10.1134/S0361768822020037zbMath1498.37097OpenAlexW4224305822WikidataQ114075144 ScholiaQ114075144MaRDI QIDQ2142971

A. B. Batkhin

Publication date: 30 May 2022

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

Full work available at URL: https://doi.org/10.1134/s0361768822020037

zbMATH Keywords

homological equationsHill probleminvariant normalization

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Uses Software

• Mathematica

Cites Work

• Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem
• An algorithm to generate canonical transformations: Application to normal forms
• Hamiltonian normalization in the restricted many-body problem by computer algebra methods
• Web of families of periodic orbits of the generalized Hill problem
• Algorithms and programs for calculating the roots of polynomial of one or two variables
• Invariant normalization of non-autonomous Hamiltonian systems
• A Methodology for the Numerical Computation of Normal Forms, Centre Manifolds and First Integrals of Hamiltonian Systems
• Canonical transformations depending on a small parameter
• Expansion formulae in canonical transformations depending on a small parameter
• A new algorithm for the Lie transformation
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