On generalizations of the pentagram map: discretizations of AGD flows

2011/03/25 by Gloria Marı́ Beffa, Gloria Mari Beffa, Beffa, Gloria Mari
Engineering · Mathematics · Physics and Astronomy · #37K10 #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math-ph #math.MP #msc:37K10

paper · pdf · doi:10.48550/arxiv.1103.5047

arxiv created 2011/03/25 · openalex publication_date 2011/03/25 · arxiv updated 2011/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate discretizations of AGD flows whose projective realizations are defined by intersecting different types of subspaces in \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 k-AGD flow in m dimensions can be discretized using one k-1 subspace and k-1 different m-1-dimensional subspaces of \RP^m.

Citations

• Discrete monodromy, pentagrams, and the method of condensation
• The Pentagram Map: A Discrete Integrable System

Related

• The Pentagram map in higher dimensions and KdV flows
• Long-diagonal pentagram maps
• The Pentagram map: a discrete integrable system
• Integrability of higher pentagram maps
• Pentagram maps over rings, Grassmannians, and skewers