Journal of Fixed Point Theory and Applications

, Volume 3, Issue 2, pp 379–409

Discrete monodromy, pentagrams, and the method of condensation


DOI: 10.1007/s11784-008-0079-0

Cite this article as:
Schwartz, R.E. J. fixed point theory appl. (2008) 3: 379. doi:10.1007/s11784-008-0079-0


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.

Mathematics Subject Classification (2000).



Polygonpentagrammonodromycross ratiodeterminants

Copyright information

© Birkhaeuser 2008

Authors and Affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA