Examples of nonintegrable Hamiltonians in real analytic mechanics
type: Item
instance of: scholarly article
title: Examples of nonintegrable Hamiltonians in real analytic mechanics
zbMATH Open document ID: 1042.37039
author: Michèle Audin
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2004-06-14T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73598
review text: Using the meromorphic nonintegrability theorems of \textit{S. L. Ziglin} [Funct. Anal. Appl. 16, 181--189 (1983; Zbl 0524.58015) and ibid. 17, 6--17 (1983; Zbl 0518.58016)] and \textit{J. Morales-Ruiz} and \textit{J. P. Ramis} [Methods Appl. Anal. 8, 33--95 (2001; Zbl 1140.37352) and ibid. 8, 97--111 (2001; Zbl 1140.37354)] several examples of real nonintegrable Hamiltonian systems on (open subsets of) \(\mathbb R^4\) are presented. Among them, there are two remarkable, namely Hénon-Heiles and Yang-Mills with the gauge group \(SU(2)\).
Mathematics Subject Classification ID: 37J30
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 70H07
zbMATH DE Number: 2074285
zbMATH Keywords: integrability of Hamiltonian systems
zbMATH Keywords: differential Galois theory
zbMATH Keywords: Lamé equations
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
OpenAlex ID: W4302617457
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DOI: 10.5802/AFST.1042
description: scientific article; zbMATH DE number 2074285