Linear difference equations, frieze patterns, and the combinatorial Gale transform
Linear difference equations, frieze patterns, and the combinatorial Gale transform
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线性差分方程、饰带图案和组合 Gale 变换
DOI：
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发表时间：
2014
期刊：
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通讯作者：
S. Tabachnikov
中科院分区：
文献类型：
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作者：
S. Morier;V. Ovsienko;Richard EVAN SCHWARTZ;S. Tabachnikov
摘要研究了具有周期系数的线性差分方程空间及其（反）周期解。我们证明了该空间与单调条纹空间同构，并与射影空间中点的组态模空间密切相关。我们定义了组合Gale变换的概念，它是不同阶周期差分方程之间的对偶性。我们将经典高斯映射推广到周期有理映射。
Abstract We study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of a combinatorial Gale transform, which is a duality between periodic difference equations of different orders. We describe periodic rational maps generalizing the classical Gauss map.