A note on uniqueness of the normal form for quasi-integrable systems
type: Item
instance of: scholarly article
title: A note on uniqueness of the normal form for quasi-integrable systems
zbMATH Open document ID: 0768.58043
DOI: 10.1007/BF00424367
author: Jan Herczyński
published in: Meccanica
publication date: 1993-04-01T00:00:00Z
review text: The paper provides a proof of the fact that at non-resonant actions the normal form for a quasi-integrable Hamiltonian system, as defined by von Zeipel-Poincaré and Lie perturbation algorithms is unique. The proof is based upon analyticity and therefore it overcomes some algebraic difficulties.
reviewed by: Themistocles M. Rassias
Mathematics Subject Classification ID: 37G05
zbMATH DE Number: 148337
zbMATH Keywords: quasi-integrable systems
zbMATH Keywords: Hamiltonian perturbation theory
zbMATH Keywords: Lie algorithm
zbMATH Keywords: measure zero
zbMATH Keywords: formal power series
zbMATH Keywords: trigonometric polynomials
zbMATH Keywords: Fourier components
MaRDI profile type: Publication
cites work: Equivalence of the generalized Lie-Hori method and the method of averaging
cites work: Canonical transformations depending on a small parameter
cites work: Formal integrals for an autonomous Hamiltonian system near an equilibrium point
cites work: On a perturbation theory using Lie transforms
cites work: Regular and stochastic motion
cites work: The uniqueness of normal forms via Lie transforms and its applications to Hamiltonian systems
cites work: Explicit recursive algorithms for the construction of equivalent canonical transformations
cites work: A relation between Giorgilli-Galgani's and Deprit's algorithms
cites work: The equivalence of von Zeipel mappings and Lie transforms
cites work: Kruskal's Perturbation Method
description: scientific article; zbMATH DE number 148337