Linear difference equations, frieze patterns and combinatorial Gale transform
Combinatorics
2013-09-17 v1 Differential Geometry
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 combinatorial Gale transform which is a duality between periodic difference equations of different orders. We describe periodic rational maps generalizing the classical Gauss map.
Cite
@article{arxiv.1309.3880,
title = {Linear difference equations, frieze patterns and combinatorial Gale transform},
author = {Sophie Morier-Genoud and Valentin Ovsienko and Richard Evan Schwartz and Serge Tabachnikov},
journal= {arXiv preprint arXiv:1309.3880},
year = {2013}
}