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The pentagram map in higher dimensions and KdV flows
1. | School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA and Department of Mathematics,, University of Toronto, Toronto, ON M5S 2E4, Canada |
2. | Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada |
References:
[1] |
M. Gekhtman, M. Shapiro, S. Tabachnikov and A. Vainshtein, Higher pentagram maps, weighted directed networks, and cluster dynamics, Electron. Res. Announc. Math. Sci., 19 (2012), 1-17; arXiv:1110.0472. |
[2] |
B. Khesin and F. Soloviev, Integrability of higher pentagram maps, (2012); arXiv:1204.0756. |
[3] |
I. M. Krichever and D. H. Phong, On the integrable geometry of soliton equations and N=2 supersymmetric gauge theories, J. Diff. Geom., 45 (1997), 349-389. |
[4] |
I. M. Krichever and D. H. Phong, Symplectic forms in the theory of solitons, in "Surveys in Differential Geometry: Integral Systems [Integrable Systems]," Surv. Diff. Geom., Vol. IV, Int. Press, Boston, MA, (1998), 239-313. |
[5] |
G. Marí Beffa, On generalizations of the pentagram map: Discretizations of AGD flows, (2011); arXiv:1103.5047. |
[6] |
V. Ovsienko, R. Schwartz and S. Tabachnikov, The pentagram map: A discrete integrable system, Comm. Math. Phys., 299 (2010), 409-446; arXiv:0810.5605.
doi: 10.1007/s00220-010-1075-y. |
[7] |
V. Ovsienko, R. Schwartz and S. Tabachnikov, Liouville-Arnold integrability of the pentagram map on closed polygons, (2011); arXiv:1107.3633. |
[8] |
R. Schwartz, The pentagram map, Experiment. Math., 1 (1992), 71-81. |
[9] |
F. Soloviev, Integrability of the pentagram map, submitted to Duke Mathematical Journal, (2011); arXiv:1106.3950. |
show all references
References:
[1] |
M. Gekhtman, M. Shapiro, S. Tabachnikov and A. Vainshtein, Higher pentagram maps, weighted directed networks, and cluster dynamics, Electron. Res. Announc. Math. Sci., 19 (2012), 1-17; arXiv:1110.0472. |
[2] |
B. Khesin and F. Soloviev, Integrability of higher pentagram maps, (2012); arXiv:1204.0756. |
[3] |
I. M. Krichever and D. H. Phong, On the integrable geometry of soliton equations and N=2 supersymmetric gauge theories, J. Diff. Geom., 45 (1997), 349-389. |
[4] |
I. M. Krichever and D. H. Phong, Symplectic forms in the theory of solitons, in "Surveys in Differential Geometry: Integral Systems [Integrable Systems]," Surv. Diff. Geom., Vol. IV, Int. Press, Boston, MA, (1998), 239-313. |
[5] |
G. Marí Beffa, On generalizations of the pentagram map: Discretizations of AGD flows, (2011); arXiv:1103.5047. |
[6] |
V. Ovsienko, R. Schwartz and S. Tabachnikov, The pentagram map: A discrete integrable system, Comm. Math. Phys., 299 (2010), 409-446; arXiv:0810.5605.
doi: 10.1007/s00220-010-1075-y. |
[7] |
V. Ovsienko, R. Schwartz and S. Tabachnikov, Liouville-Arnold integrability of the pentagram map on closed polygons, (2011); arXiv:1107.3633. |
[8] |
R. Schwartz, The pentagram map, Experiment. Math., 1 (1992), 71-81. |
[9] |
F. Soloviev, Integrability of the pentagram map, submitted to Duke Mathematical Journal, (2011); arXiv:1106.3950. |
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