Integrable cluster dynamics of directed networks and pentagram maps
From MaRDI portal
Publication:304096
DOI10.1016/j.aim.2016.03.023zbMath1360.37148arXiv1406.1883OpenAlexW2331547418MaRDI QIDQ304096
Michael Shapiro, A. D. Vaĭnshteĭn, Sergei Tabachnikov, Michael I. Gekhtman
Publication date: 23 August 2016
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1406.1883
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Cluster algebras (13F60)
Related Items
A generalization of Laurent biorthogonal polynomials and related integrable lattices, Solutions to the T-systems with principal coefficients, Toric networks, geometric \(R\)-matrices and generalized discrete Toda lattices, Pentagrams, inscribed polygons, and Prym varieties, Dimers, networks, and cluster integrable systems, 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, Projective self-dual polygons in higher dimensions, Long‐diagonal pentagram maps, Discrete dynamics in cluster integrable systems from geometric \(R\)-matrix transformations, Non-commutative integrability of the Grassmann pentagram map, On the domino shuffle and matrix refactorizations, Vector-relation configurations and plabic graphs, Polygon recutting as a cluster integrable system, Projective Configuration Theorems: Old Wine into New Wineskins, Open problems, questions and challenges in finite- dimensional integrable systems, Difference equations arising from cluster algebras, Solution of tetrahedron equation and cluster algebras, Kasteleyn operators from mirror symmetry, Quivers with additive labelings: classification and algebraic entropy, Linear difference equations, frieze patterns, and the combinatorial Gale transform
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On singularity confinement for the pentagram map
- Liouville-Arnold integrability of the pentagram map on closed polygons
- Integrability of higher pentagram maps
- Integrability of the pentagram map
- Poisson geometry of directed networks in an annulus
- Higher pentagram maps, weighted directed networks, and cluster dynamics
- The devron property
- \(T\)-systems and the pentagram map
- Non-integrability vs. integrability in pentagram maps
- The pentagram integrals for Poncelet families
- The pentagram map and \(Y\)-patterns
- Elementary surprises in projective geometry
- The pentagram integrals on inscribed polygons
- Generalized Bäcklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective
- Circle patterns with the combinatorics of the square grid
- The pentagram map in higher dimensions and KdV flows
- Discrete monodromy, pentagrams, and the method of condensation
- Integrable deformations of a polygon
- Quasiperiodic motion for the pentagram map
- Discrete versions of some classical integrable systems and factorization of matrix polynomials
- Dynamical systems VII. Integrable systems. Nonholonomic dynamical systems. Transl. from the Russian by A.G. Reyman and M.A. Semenov-Tian- Shansky
- Recuttings of polygons
- Hexagonal circle patterns and integrable systems: Patterns with constant angles
- The problem of integrable discretization: Hamiltonian approach
- On generalizations of the pentagram map: discretizations of AGD flows
- Poisson geometry of directed networks in a disk
- The geometry of dented pentagram maps
- Dual moment maps into loop algebras
- The Pentagram Map is Recurrent
- Cluster algebras IV: Coefficients
- Integrable maps
- On some integrable systems related to the Toda lattice
- Multiple Hamiltonian structures for Toda-type systems
- Loop Groups, Clusters, Dimers and Integrable Systems
- Dimers and cluster integrable systems
- On Integrable Generalizations of the Pentagram Map
- The pentagram map: a discrete integrable system
