, Volume 3, Issue 2, pp 379-409
Date: 25 Jul 2008

Discrete monodromy, pentagrams, and the method of condensation

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Abstract.

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.

I dedicate this paper to Professor V. I. Arnold on the occasion of his 70th birthday