The center-focus problem and reversibility (Q5944088)
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scientific article; zbMATH DE number 1649177
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The center-focus problem and reversibility |
scientific article; zbMATH DE number 1649177 |
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The center-focus problem and reversibility (English)
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29 September 2002
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center
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focus
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involution
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reversibility
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analytic vector field
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monodromy conditions
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normal forms
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The reversibility is an interesting concept useful in the qualitative theory of differential equations that implies certain geometric properties. For instance, if an orbit of a reversible vector field meets the fixed-point set at two distinct points then it is necessarily a symmetric periodic orbit. NEWLINENEWLINENEWLINEThe paper is concerned with the following problem for a class of two-dimensional systems having a center at the singular point: if a system possesses certain symmetries, what can be said about its reversibility? Sufficient and necessary conditions for the analytic planar system to have a center are given and the reversibility of certain classes of polynomial vector fields is discussed.
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