Schwartz, Richard Evan Discrete monodromy, pentagrams, and the method of condensation. (English) Zbl 1148.51001 J. Fixed Point Theory Appl. 3, No. 2, 379-409 (2008). Summary: This paper studies the pentagram map, a projectively natural iteration on the space of polygons. Inspired by a method from the theory of ordinary differential equations, the paper constructs roughly \(n\) algebraically independent invariants for the map, when it is defined on the space of \(n\)-gons. These invariants strongly suggest that the pentagram map is a discrete completely integrable system. The paper also relates the pentagram map to Dodgson’s method of condensation for computing determinants, also known as the octahedral recurrence. Cited in 3 ReviewsCited in 27 Documents MSC: 51A05 General theory of linear incidence geometry and projective geometries 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 52A10 Convex sets in \(2\) dimensions (including convex curves) Keywords:polygon; pentagram; monodromy; cross ratio; determinants Software:Mathematica PDFBibTeX XMLCite \textit{R. E. Schwartz}, J. Fixed Point Theory Appl. 3, No. 2, 379--409 (2008; Zbl 1148.51001) Full Text: DOI arXiv