The pentagram map is a completely integrable system defined on the moduli space of polygons. The integrals for the system are certain weighted homogeneous polynomials, which come in pairs: E1,O2,E2,O2,... In this paper we prove that Ek = Ok for all k, when these integrals are restricted to the space of polygons which are inscribed in a conic section. Our proof is essentially a combinatorial analysis of the integrals.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics