{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T10:29:27Z","timestamp":1762079367940},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,12,13]],"date-time":"2012-12-13T00:00:00Z","timestamp":1355356800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2013,4]]},"DOI":"10.1007\/s00332-012-9152-3","type":"journal-article","created":{"date-parts":[[2012,12,12]],"date-time":"2012-12-12T18:50:21Z","timestamp":1355338221000},"page":"303-334","source":"Crossref","is-referenced-by-count":23,"title":["On Generalizations of the Pentagram Map: Discretizations of AGD Flows"],"prefix":"10.1007","volume":"23","author":[{"given":"Gloria","family":"Mar\u00ed\u00a0Beffa","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,12,13]]},"reference":[{"key":"9152_CR1","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF01410079","volume":"50","author":"M. Adler","year":"1979","unstructured":"Adler, M.: On a trace functional for formal pseudo-differential operators and the symplectic structure of the KdV. Invent. Math. 50, 219\u2013248 (1979)","journal-title":"Invent. Math."},{"key":"9152_CR2","doi-asserted-by":"crossref","unstructured":"Calini, A., Ivey, T., Mar\u00ed Beffa, G.: An integrable flow for starlike curves in centroaffine space (2012, submitted)","DOI":"10.3842\/SIGMA.2013.022"},{"key":"9152_CR3","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1142\/S0129055X9900026X","volume":"11","author":"R. Dickson","year":"1999","unstructured":"Dickson, R., Gesztesy, F., Unterkoer, K.: Algebro-geometric solutions of the Boussinesq hierarchy. Rev. Math. Phys. 11, 823\u2013879 (1999)","journal-title":"Rev. Math. Phys."},{"key":"9152_CR4","series-title":"Itogi Nauki i Tekhniki","first-page":"81","volume-title":"Current Problems in Mathematics","author":"V.G. Drinfel\u2019d","year":"1984","unstructured":"Drinfel\u2019d, V.G., Sokolov, V.V.: Lie algebras and equations of Korteweg\u2013de Vries type. In: Current Problems in Mathematics. Itogi Nauki i Tekhniki, vol. 24, pp. 81\u2013180. Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform, Moscow (1984)"},{"key":"9152_CR5","doi-asserted-by":"crossref","unstructured":"Fels, M., Olver, P.J.: Moving coframes. II. Regularization and theoretical foundations. Acta Appl. Math., 127\u2013208 (1999)","DOI":"10.1023\/A:1006195823000"},{"key":"9152_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61705-8","volume-title":"Collected Papers","author":"I.M. Gel\u2019fand","year":"1987","unstructured":"Gel\u2019fand, I.M., Dickey, L.A.: A family of Hamiltonian structures connected with integrable nonlinear differential equations. In: Gelfand, I.M. (ed.) Collected Papers, vol. 1. Springer, Berlin (1987)"},{"key":"9152_CR7","first-page":"1","volume":"19","author":"M. Gekhtman","year":"2012","unstructured":"Gekhtman, M., Shapiro, M., Tabachnikov, S., Vainshtein, A.: Higher pentagram maps, weighted directed networks, and cluster dynamics. Electron. Res. Announc. Math. Sci. 19, 1\u201317 (2012)","journal-title":"Electron. Res. Announc. Math. Sci."},{"key":"9152_CR8","doi-asserted-by":"crossref","first-page":"5720","DOI":"10.1063\/1.532162","volume":"38","author":"R. Heredero","year":"1997","unstructured":"Heredero, R., Lopez, A., Mar\u00ed Beffa, G.: Invariant differential equations and the Adler\u2013Gel\u2019fand\u2013Dikii bracket. J. Math. Phys. 38, 5720\u20135738 (1997)","journal-title":"J. Math. Phys."},{"key":"9152_CR9","unstructured":"Hubert, E.: Generation properties of differential invariants in the moving frame methods. Preprint http:\/\/hal.inria.fr\/inria-00194528\/en (2007)"},{"key":"9152_CR10","doi-asserted-by":"crossref","unstructured":"Khesin, B., Soloviev, F.: Integrability of higher pentagram maps (2012a). arXiv:1204.0756","DOI":"10.1007\/s00208-013-0922-5"},{"key":"9152_CR11","doi-asserted-by":"crossref","unstructured":"Khesin, B., Soloviev, F.: The pentagram map in higher dimensions and KdV flows (2012b). arXiv:1205.3744","DOI":"10.3934\/era.2012.19.86"},{"key":"9152_CR12","doi-asserted-by":"crossref","unstructured":"Lobb, S.B., Nijhoff, F.W.: Lagrangian multiform structure for the lattice Gel\u2019fand\u2013Dikii hierarchy. J. Phys. A 43(7) (2010)","DOI":"10.1088\/1751-8113\/43\/7\/072003"},{"key":"9152_CR13","doi-asserted-by":"crossref","first-page":"363","DOI":"10.24033\/bsmf.2353","volume":"127","author":"G. Mar\u00ed Beffa","year":"1999","unstructured":"Mar\u00ed Beffa, G.: The theory of differential invariants and KdV Hamiltonian evolutions. Bull. Soc. Math. Fr. 127, 363\u2013391 (1999)","journal-title":"Bull. Soc. Math. Fr."},{"key":"9152_CR14","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1090\/S0002-9939-05-07998-0","volume":"134","author":"G. Mar\u00ed Beffa","year":"2006","unstructured":"Mar\u00ed Beffa, G.: Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces. Proc. Am. Math. Soc. 134, 779\u2013791 (2006)","journal-title":"Proc. Am. Math. Soc."},{"issue":"1","key":"9152_CR15","first-page":"1","volume":"12","author":"G. Mar\u00ed Beffa","year":"2008","unstructured":"Mar\u00ed Beffa, G.: Geometric Hamiltonian structures on flat semisimple homogeneous manifolds, the Asian. J. Math. 12(1), 1\u201333 (2008)","journal-title":"J. Math."},{"issue":"1","key":"9152_CR16","doi-asserted-by":"crossref","first-page":"163","DOI":"10.2140\/pjm.2010.247.163","volume":"247","author":"G. Mar\u00ed Beffa","year":"2010","unstructured":"Mar\u00ed Beffa, G.: On bi-Hamiltonian flows and their realizations as curves in real semisimple homogeneous manifolds. Pac. J. Math. 247(1), 163\u2013188 (2010)","journal-title":"Pac. J. Math."},{"key":"9152_CR17","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s00220-010-1075-y","volume":"299","author":"V. Ovsienko","year":"2010","unstructured":"Ovsienko, V., Schwartz, R., Tabachnikov, S.: The pentagram map: a discrete integrable system. Commun. Math. Phys. 299, 409\u2013446 (2010)","journal-title":"Commun. Math. Phys."},{"key":"9152_CR18","unstructured":"Ovsienko, V., Schwartz, R., Tabachnikov, S.: Liouville\u2013Arnold Integrability of the pentagram map on closed polygons (2011). arXiv:1107.3633"},{"key":"9152_CR19","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1080\/10586458.2001.10504671","volume":"10.4","author":"R. Schwartz","year":"2001","unstructured":"Schwartz, R.: The pentagram map is recurrent. J. Exp. Math. 10.4, 519\u2013528 (2001)","journal-title":"J. Exp. Math."},{"key":"9152_CR20","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s11784-008-0079-0","volume":"3","author":"R. Schwartz","year":"2008","unstructured":"Schwartz, R.: Discrete monodromy, pentagrams and the method of condensation. J. Fixed Point Theory Appl. 3, 379\u2013409 (2008)","journal-title":"J. Fixed Point Theory Appl."},{"issue":"1","key":"9152_CR21","doi-asserted-by":"crossref","DOI":"10.37236\/658","volume":"18","author":"R. Schwartz","year":"2011","unstructured":"Schwartz, R., Tabachnikov, S.: The pentagram integrals for inscribed polygons. Electron. J. Combin. 18(1), 171 (2011)","journal-title":"Electron. J. Combin."},{"key":"9152_CR22","unstructured":"Soloviev, F.: Integrability of the pentagram map (2011). arXiv:1106.3950"},{"key":"9152_CR23","volume-title":"Projective Differential Geometry of Curves and Ruled Surfaces","author":"E.J. Wilczynski","year":"1906","unstructured":"Wilczynski, E.J.: Projective Differential Geometry of Curves and Ruled Surfaces. Teubner, Leipzig (1906)"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-012-9152-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00332-012-9152-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-012-9152-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,18]],"date-time":"2020-07-18T15:08:42Z","timestamp":1595084922000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-012-9152-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,13]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,4]]}},"alternative-id":["9152"],"URL":"https:\/\/doi.org\/10.1007\/s00332-012-9152-3","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,13]]}}}