A numerical perturbation method based on the KAM construction

DOI10.1016/0167-2789(89)90106-1zbMath0688.70014OpenAlexW1993478917MaRDI QIDQ1264014

Prasenjit Saha

Publication date: 1989

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(89)90106-1

zbMATH Keywords

series expansionLie transformsnondegenerate HamiltoniansHénon's isochrone HamiltonianKAM construction

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Celestial mechanics (70F15) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Cites Work

• Hamiltonian maps in the complex plane
• Invariant tori through direct solution of the Hamilton-Jacobi equation
• Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures
• Convergent series expansions for quasi-periodic motions
• Rigorous estimates for a computer-assisted KAM theory
• An accelerated elimination technique for the solution of perturbed Hamiltonian systems
• A variational principle for invariant tori of fixed frequency
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