Examples of nonintegrable Hamiltonians in real analytic mechanics (Q1432081)
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scientific article; zbMATH DE number 2074285
| Language | Label | Description | Also known as |
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| English | Examples of nonintegrable Hamiltonians in real analytic mechanics |
scientific article; zbMATH DE number 2074285 |
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Examples of nonintegrable Hamiltonians in real analytic mechanics (English)
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14 June 2004
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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 \(SU(2)\).
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integrability of Hamiltonian systems
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differential Galois theory
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Lamé equations
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