Geodesic
Linear difference equations, frieze patterns, and the combinatorial Gale transform
Forum of Mathematics, Sigma, Tome 2 (2014)

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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. 
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     title = {Linear difference equations, frieze patterns, and the combinatorial {Gale} transform},
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SOPHIE MORIER-GENOUD; VALENTIN OVSIENKO; RICHARD EVAN SCHWARTZ; SERGE TABACHNIKOV. Linear difference equations, frieze patterns, and the combinatorial Gale transform. Forum of Mathematics, Sigma, Tome 2 (2014). doi: 10.1017/fms.2014.20

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