Equivalence for lie transforms

DOI10.1007/BF01229124zbMath0321.34036OpenAlexW2025282430MaRDI QIDQ4084041

Jacques Roels, Jacques Henrard

Publication date: 1974

Published in: Celestial Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01229124

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Differential topological aspects of diffeomorphisms (57R50)

Related Items (13)

High-order control for symplectic maps ⋮ On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms ⋮ GITA: A REDUCE program for the normalization of polynomial Hamiltonians ⋮ Lie series method for vector fields and Hamiltonian perturbation theory ⋮ Slow crossing of a stochastic layer ⋮ [https://portal.mardi4nfdi.de/wiki/Publication:4118118 Perturbations des syst�mes diff�rentiels et r�sultats de g�om�trie diff�rentielle] ⋮ A new radial, natural, higher-order intermediary of the main problem four decades after the elimination of the parallax ⋮ Algebraic aspects of perturbation theories ⋮ Resolution methods of perturbed differential equations, using tools of differential geometry ⋮ On a common derivation of the averaging method and the two-timescale method ⋮ Multiple-parameter Lie transform ⋮ Branching solutions and Lie series ⋮ Two-parameter Lie transforms

Cites Work

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• Canonical transformations depending on a small parameter
• The equivalence of von Zeipel mappings and Lie transforms
• On a perturbation theory using Lie transforms
• Explicit recursive algorithms for the construction of equivalent canonical transformations
• Perturbation method in the theory of nonlinear oscillations

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