On Generalizations of the Pentagram Map: Discretizations of AGD Flows.

In this paper we investigate discretizations of AGD flows whose projective realizations are defined by intersecting different types of subspace in $\mathbb{RP}^{m}$. These maps are natural candidates to generalize the pentagram map, itself defined as the intersection of consecutive shortest diagonals of a convex polygon, and a completely integrable discretization of the Boussinesq equation. We conjecture that the r-AGD flow in m dimensions can be discretized using one ( r−1)-dimensional subspace and r−1 different ( m−1)-dimensional subspaces of $\mathbb{RP}^{m}$. [ABSTRACT FROM AUTHOR]