Reduction of polynomial planar Hamiltonians with quadratic unperturbed part (Q2706418)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Reduction of polynomial planar Hamiltonians with quadratic unperturbed part |
scientific article |
Statements
19 March 2001
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formal integrals
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normal form
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Hamiltonian
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reduced phase space
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Reduction of polynomial planar Hamiltonians with quadratic unperturbed part (English)
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The authors classify the possible normal forms of quadratic Hamiltonian systems in two dimensions. Then they give a method to reduce by one the number of degrees of freedom of an arbitrary polynomial Hamiltonian, of which the principal part is quadratic in positions and moments. The reduction procedure is based on the extension of an integral of the unperturbed part to the whole system, up to a certain order. The corresponding reduced phase spaces have dimension 2 and are described by means of the set of invariants associated to the reduction.
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