Integrability of higher pentagram maps

DOI10.1007/s00208-013-0922-5zbMath1280.37056arXiv1204.0756OpenAlexW2963021787MaRDI QIDQ378834

Boris A. Khesin, Fedor Soloviev

Publication date: 12 November 2013

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.0756

zbMATH Keywords

symplectic leavesalgebraic-geometric integrability of pentagram mapsclosed polygonsinvariant symplectic structurepentagram maps

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)

Related Items (22)

Integrable cluster dynamics of directed networks and pentagram maps ⋮ The geometry of dented pentagram maps ⋮ Pentagrams, inscribed polygons, and Prym varieties ⋮ Liouville-Arnold integrability of the pentagram map on closed polygons ⋮ The pentagram map, Poncelet polygons, and commuting difference operators ⋮ Pentagram maps and refactorization in Poisson-Lie groups ⋮ The algebraic dynamics of the pentagram map ⋮ Pentagram-type maps and the discrete KP equation ⋮ The pentagram map on Grassmannians ⋮ Long‐diagonal pentagram maps ⋮ Commuting difference operators and the combinatorial Gale transform ⋮ Loop Groups, Clusters, Dimers and Integrable Systems ⋮ On generalizations of the pentagram map: discretizations of AGD flows ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ The devron property ⋮ \(T\)-systems and the pentagram map ⋮ Non-integrability vs. integrability in pentagram maps ⋮ The pentagram integrals for Poncelet families ⋮ Pentagram Spirals ⋮ Continuous limits of generalized pentagram maps ⋮ Y-meshes and generalized pentagram maps ⋮ Linear difference equations, frieze patterns, and the combinatorial Gale transform

Cites Work

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• Vector bundles and Lax equations on algebraic curves
• On generalizations of the pentagram map: discretizations of AGD flows
• Cluster algebras IV: Coefficients
• Spin chain models with spectral curves from M theory
• The pentagram map: a discrete integrable system

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