On Integrable Generalizations of the Pentagram Map

DOI10.1093/imrn/rnu044zbMath1321.37066arXiv1303.4295OpenAlexW2963856897MaRDI QIDQ5500410

Gloria Marí Beffa

Publication date: 6 August 2015

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.4295

zbMATH Keywords

integrabilityscaling invarianceLax representationpentagram map

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) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (10)

Integrable cluster dynamics of directed networks and pentagram maps ⋮ The geometry of dented pentagram maps ⋮ Pentagrams, inscribed polygons, and Prym varieties ⋮ Pentagram maps and refactorization in Poisson-Lie groups ⋮ The pentagram map on Grassmannians ⋮ Commuting difference operators and the combinatorial Gale transform ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Continuous limits of generalized pentagram maps ⋮ Y-meshes and generalized pentagram maps ⋮ Linear difference equations, frieze patterns, and the combinatorial Gale transform

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