Equivariant generating functions and periodic points (Q2741155)
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scientific article; zbMATH DE number 1642385
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equivariant generating functions and periodic points |
scientific article; zbMATH DE number 1642385 |
Statements
12 June 2002
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area-preserving maps
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resonance
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bifurcation
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Equivariant generating functions and periodic points (English)
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Let an area-preserving map have a fixed point at the origin whose multipliers are \(n\)-th roots of unity, \(n\geq 2\). Then there is a function \(L\) whose critical points (excepting the origin) correspond to periodic points of the map of period \(n\). A maximum or minimum corresponds to an elliptic orbit and a saddle point correspond to a hyperbolic orbit. After a change of coordinates the function \(L\) is symmetric with respect to rotation by \(2\pi/n\).NEWLINENEWLINEFor the entire collection see [Zbl 0963.00030].
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