The pentagram integrals for Poncelet families
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Publication:478641
DOI10.1016/j.geomphys.2014.07.024zbMath1309.37068OpenAlexW2036292436MaRDI QIDQ478641
Publication date: 3 December 2014
Published in: Journal of Geometry and Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.geomphys.2014.07.024
Polyhedra and polytopes; regular figures, division of spaces (51M20) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Projective techniques in algebraic geometry (14N05)
Related Items (6)
Integrable cluster dynamics of directed networks and pentagram maps ⋮ Pentagrams, inscribed polygons, and Prym varieties ⋮ Poncelet-Darboux, Kippenhahn, and Szegő: interactions between projective geometry, matrices and orthogonal polynomials ⋮ The pentagram map, Poncelet polygons, and commuting difference operators ⋮ Projective self-dual polygons in higher dimensions ⋮ Billiards in ellipses revisited
Cites Work
- Liouville-Arnold integrability of the pentagram map on closed polygons
- 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 map in higher dimensions and KdV flows
- Discrete monodromy, pentagrams, and the method of condensation
- Quasiperiodic motion for the pentagram map
- T-systems with boundaries from network solutions
- On generalizations of the pentagram map: discretizations of AGD flows
- The geometry of dented pentagram maps
- The Pentagram Map is Recurrent
- Loop Groups, Clusters, Dimers and Integrable Systems
- The Poncelet grid
- The pentagon in the projective plane, with a comment on Napier’s rule
- The pentagram map: a discrete integrable system
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