Linear difference equations, frieze patterns, and the combinatorial Gale transform

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...

Full description

Saved in:
Bibliographic Details
Published in:Forum of mathematics. Sigma 2014-08, Vol.2, Article e22
Main Authors: MORIER-GENOUD, SOPHIE, OVSIENKO, VALENTIN, EVAN SCHWARTZ, RICHARD, TABACHNIKOV, SERGE
Format: Article
Language:English
Subjects:
13F60
14M15
39A70
52B99
Discrete Mathematics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2014.20