The geometry of dented pentagram maps

DOI10.4171/JEMS/586zbMath1350.37065arXiv1308.5363MaRDI QIDQ2633998

Fedor Soloviev, Boris A. Khesin

Publication date: 5 February 2016

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.5363

zbMATH Keywords

Lax representationspace polygonsalgebraic-geometric integrabilityPentagram maps

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Projective differential geometry (53A20)

Related Items (15)

Integrable cluster dynamics of directed networks and pentagram maps ⋮ Pentagrams, inscribed polygons, and Prym varieties ⋮ The pentagram map, Poncelet polygons, and commuting difference operators ⋮ Pentagram maps and refactorization in Poisson-Lie groups ⋮ Pentagram-type maps and the discrete KP equation ⋮ Projective self-dual polygons in higher dimensions ⋮ The pentagram map on Grassmannians ⋮ Long‐diagonal pentagram maps ⋮ Commuting difference operators and the combinatorial Gale transform ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ The pentagram integrals for Poncelet families ⋮ Continuous limits of generalized pentagram maps ⋮ Y-meshes and generalized pentagram maps ⋮ Lagrangian configurations and symplectic cross-ratios ⋮ Linear difference equations, frieze patterns, and the combinatorial Gale transform

Cites Work

• Integrability of higher pentagram maps
• Integrability of the pentagram map
• Higher pentagram maps, weighted directed networks, and cluster dynamics
• Non-integrability vs. integrability in pentagram maps
• The pentagram map and \(Y\)-patterns
• Discrete monodromy, pentagrams, and the method of condensation
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• General rational reductions of the KP hierarchy and their symmetries
• On generalizations of the pentagram map: discretizations of AGD flows
• On Integrable Generalizations of the Pentagram Map
• The pentagram map: a discrete integrable system
• Unnamed Item

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