Liouville-Arnold integrability of the pentagram map on closed polygons
From MaRDI portal
Publication:374592
DOI10.1215/00127094-2348219zbMath1315.37035arXiv1107.3633OpenAlexW3099292260MaRDI QIDQ374592
Valentin Ovsienko, Sergei Tabachnikov, Richard Evan Schwartz
Publication date: 23 October 2013
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1107.3633
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Configuration theorems in linear incidence geometry (51A20)
Related Items
Integrable cluster dynamics of directed networks and pentagram maps, A first integrability result for Miquel dynamics, Pentagrams, inscribed polygons, and Prym varieties, Pentagram Configurations for Pentagons and Hexagons, On singularity confinement for the pentagram map, Integrability of higher pentagram maps, The pentagram map, Poncelet polygons, and commuting difference operators, Pentagram maps and refactorization in Poisson-Lie groups, Integrability of the pentagram map, The algebraic dynamics of the pentagram map, Pentagram-type maps and the discrete KP equation, On the dynamics of the line operator \(\Lambda_{\{2\},\{3\}}\) on some arrangements of six lines, The pentagram map on Grassmannians, Commuting difference operators and the combinatorial Gale transform, Loop Groups, Clusters, Dimers and Integrable Systems, Legendrian weaves: \(N\)-graph calculus, flag moduli and applications, On generalizations of the pentagram map: discretizations of AGD flows, Projective Configuration Theorems: Old Wine into New Wineskins, Open problems, questions and challenges in finite- dimensional integrable systems, \(T\)-systems and the pentagram map, Coxeter's frieze patterns and discretization of the Virasoro orbit, The pentagram integrals for Poncelet families, 2-frieze patterns and the cluster structure of the space of polygons, Y-meshes and generalized pentagram maps, Lagrangian configurations and symplectic cross-ratios, 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
- Integrability of higher pentagram maps
- Integrability of the pentagram map
- Higher pentagram maps, weighted directed networks, and cluster dynamics
- The pentagram map and \(Y\)-patterns
- Elementary surprises in projective geometry
- The pentagram integrals on inscribed polygons
- The pentagram map in higher dimensions and KdV flows
- 2-frieze patterns and the cluster structure of the space of polygons
- Discrete monodromy, pentagrams, and the method of condensation
- Quasiperiodic motion for the pentagram map
- Drinfeld-Sokolov reduction for difference operators and deformations of \({\mathcal W}\)-algebras. I: The case of Virasoro algebra
- On generalizations of the pentagram map: discretizations of AGD flows
- Cluster algebras I: Foundations
- The Pentagram Map is Recurrent
- Loop Groups, Clusters, Dimers and Integrable Systems
- Lagrangian multiform structure for the lattice Gel'fand–Dikii hierarchy
- Analytic theory of difference equations with rational and elliptic coefficients and the Riemann-Hilbert problem
- THE BOUSSINESQ INTEGRABLE SYSTEM: COMPATIBLE LATTICE AND CONTINUUM STRUCTURES
- The pentagon in the projective plane, with a comment on Napier’s rule
- The pentagram map: a discrete integrable system