A period formula for torus automorphisms (Q1395996)
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scientific article; zbMATH DE number 1941563
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A period formula for torus automorphisms |
scientific article; zbMATH DE number 1941563 |
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A period formula for torus automorphisms (English)
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18 February 2004
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The paper determines the order of integer matrices \(A\in SL_2 (\mathbb{Z})\) on lattices \(L_N={1 \over N}\mathbb{Z}^2/ \mathbb{Z}^2\) of \(\mathbb{Q}^2/ \mathbb{Z}^2\), for \(N=P_n\equiv\) the number of \(n\)-periodic points (for the particular matrix-action on the rational 2-torus). The arguments lean heavily on arithmetical properties of (integer specializations of) certain Chebychev polynomials.
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discrete dynamical systems
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finite orbit structure
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torus automorphisms
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periods of integer matrix actions
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Chebychev polynomials
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