2021/11/16 by Richard Evan Schwartz, Schwartz, Richard Evan · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2111.08358
openalex publication_date 2021/11/16 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
In this paper I will establish a special case of a conjecture that intertwines the deep diagonal pentagram maps and Poncelet polygons. The special case is that of the 3-diagonal map acting on affine equivalence classes of centrally symmetric octagons. This is the simplest case that goes beyond an analysis of elliptic curves. The proof involves establishing that the map is Arnold-Liouville integrable in this case, and then exploring the Lagrangian surface foliation in detail.