Discrete monodromy, pentagrams, and the method of condensation
- First Online:
- 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.