A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential (Q1112634)
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scientific article; zbMATH DE number 4078877
| Language | Label | Description | Also known as |
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| English | A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential |
scientific article; zbMATH DE number 4078877 |
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A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential (English)
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1987
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A criterion, for the non-integrability of Hamiltonians with two degrees of freedom and a homogeneous potential of integer degree is derived. It is based on Ziglin's theorem [see \textit{S. L. Ziglin}, Funct. Anal. Appl. 16, 181-189 (1983; Zbl 0524.58015) and ibid. 17, 6-17 (1983; Zbl 0518.58016)] which is presented with proof in a self-contained way. Several well-known examples (anisotropic Kepler problem, 1-D Newtonian three-body problem) are presented explicitly.
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non-integrability of Hamiltonians
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homogeneous potential
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anisotropic Kepler problem
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Newtonian three-body problem
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