Classification of the phase portrait for a planar \(Z_8\)-equivariant Hamiltonian system of degree 7 (Q2780925)
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scientific article; zbMATH DE number 1720126
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of the phase portrait for a planar \(Z_8\)-equivariant Hamiltonian system of degree 7 |
scientific article; zbMATH DE number 1720126 |
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9 March 2003
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Hamiltonian system
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equivariant vector field
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phase portrait
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0.85778666
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0.8575231
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0.8523237
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0.8469399
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0.84067357
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0.8391476
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Classification of the phase portrait for a planar \(Z_8\)-equivariant Hamiltonian system of degree 7 (English)
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Here, the authors consider a \(Z_{8}\)-equivariant planar Hamiltonian vector field of degree~7. Using qualitative and numerical methods, they study the six-dimensional parameter space of the vector field and obtain the following results: 1)~there are seven cases concerning the number of fixed-points of this vector field in a finite part of the phase plane; 2)~there are fifty possible phase portraits of the vector field in these cases.
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