Singularity confinement for matrix discrete Painleve equations
| dc.contributor.author | Cassatella-Contra, Giovanni A | |
| dc.contributor.author | Mañas Baena, Manuel Enrique | |
| dc.contributor.author | Tempesta, Piergiulio | |
| dc.date.accessioned | 2023-06-19T14:54:45Z | |
| dc.date.available | 2023-06-19T14:54:45Z | |
| dc.date.issued | 2014-09 | |
| dc.description | ©IOP Publishing Ltd. PT has been supported by Spanish 'Ministerio de Ciencia e Innovacion' grant FIS2011-00260. GC-C benefitted from the financial support of a 'Accion Especial' Ref. AE1/13-18837 of the Universidad Complutense de Madrid. MM acknowledges economical support from the Spanish 'Ministerio de Economia y Competitividad' research project MTM2012-36732-C03-01, Ortogonalidad y aproximacion; Teoria y Aplicaciones. | |
| dc.description.abstract | We study the analytic properties of a matrix discrete system introduced by Cassatella and Manas (2012 Stud. Appl. Math. 128 252-74). The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters except possibly for algebraic subvarieties. This paves the way to a generalization of Painleve analysis to discrete matrix models. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovacion | |
| dc.description.sponsorship | Universidad Complutense de Madrid | |
| dc.description.sponsorship | Ministerio de Economia y Competitividad | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/30967 | |
| dc.identifier.doi | 10.1088/0951-7715/27/9/2321 | |
| dc.identifier.issn | 0951-7715 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1088/0951-7715/27/9/2321 | |
| dc.identifier.relatedurl | http://iopscience.iop.org | |
| dc.identifier.relatedurl | http://arxiv.org/abs/1311.0557 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/34735 | |
| dc.issue.number | 9 | |
| dc.journal.title | Nonlinearity | |
| dc.language.iso | eng | |
| dc.page.final | 2335 | |
| dc.page.initial | 2321 | |
| dc.publisher | IOP Publishing Ltd | |
| dc.relation.projectID | FIS2011-00260 | |
| dc.relation.projectID | AE1/13-18837 | |
| dc.relation.projectID | MTM2012-36732-C03-01 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Orthogonal polynomials | |
| dc.subject.keyword | Difference-equations | |
| dc.subject.keyword | Integrable systems | |
| dc.subject.keyword | Property | |
| dc.subject.keyword | Gravity | |
| dc.subject.keyword | Graphs | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Singularity confinement for matrix discrete Painleve equations | |
| dc.type | journal article | |
| dc.volume.number | 27 | |
| dcterms.references | [1] M. J. Ablowitz, R. Halburd, B. Herbst, On the extension of the Painleve property to difference equations. Nonlinearity 13, 889-905 (2000). [2] M. Adler, P. van Moerbeke, P. Vanhaecke, Singularity confinement for a class of m-th order difference equations of combinatorics. Philosophical Transactions of the Royal Society of London A 366, 877-922 (2008). [3] D. Arinkin, A. Borodin, Moduli spaces of d-connections and difference Painlevé equations. Duke Mathematical Journal 134, 515-556 (2006). [4] M. P. Bellon, C.-M. Viallet, Algebraic entropy, Communications in Mathematical Physics 204, 425-437 (1999). [5] A. I. Bobenko, Y. Suris, Discrete differential geometry. Integrable structure, Graduate Studies in Mathematics, 98. American Mathematical Society, Providence, RI, xxiv+404 pp. (2008). [6] A. I. Bobenko and Y. Suris, Integrable systems on quad–graphs, International Mathematical Research Notices 11, 573-611 (2002). [7] G. A. Cassatella-Contra, M. Mañas, Riemann–Hilbert problems, matrix orthogonal polynomals and discrete matrix equations with singularity confinement, Stud. Appl. Math, 128, 252-274 (2012). [8] R. Conte (Editor), The Painlevé Property. One Century Later, Springer–Verlag, New York (1999). [9] I. Dynnikov and S. P. Novikov, Geometry of the triangle equation on two–manifolds, Moscow Mathematical Journal 3, no. 2, 419-438 (2003). [10] A. S. Fokas, A. R. Its, A. V. Kitaev, Discrete Painleve equations and their appearance in quantum gravity, Communications in Mathematical Physics 142, 313344 (1991). [11] G. Freud, On the coefficients in the recursion formulae of orthogonal polynomials, Proceedings of the Royal Irish Academy A 76, 1-6 (1976). [12] B. Grammaticos, A. Ramani and V. Papageorgiou, Do integrable mappings have the Painlevé property? Physical Review Letters 67, 1825-1828 (1991). [13] J. Hietarinta and C. Viallet, Physical Review Letters 81, (1998) 325-328. [14] G. ’t Hooft, Quantization of point particles in (2+1)–dimensional gravity and spacetime discreteness, Classical and Quantum Gravity 13, 1023–1039 (1996). [15] S. Lafortune, A. Ramani, B. Grammaticos, Y. Ohta, K. M. Tamizhmani, Blending two discrete integrability criteria: singularity confinement and algebraic entropy. Bäcklund and Darboux transformations. The geometry of solitons (Halifax, NS, 1999), 299311, CRM Proceedings and Lecture Notes, 29, Amererican Mathematical Society, Providence, RI, 2001. [16] J. Moser and A. P. Veselov, Discrete versions of some classical integrable systems and factorization of matrix polynomials, Communications in Mathematical Physics 139, 217-243 (1991). [17] M. E. J. Newman, Networks, Oxford University Press, 2010. [18] S. P. Novikov, A. S. Shvarts, Discrete Lagrangian systems on graphs. Symplecto–topological properties (Russian), Uspekhi Matematicheskikh Nauk 54, no. 1 (325), 257-258 (1999); translation in Russian Math. Surveys 54, no. 1, 258–259 (1999). [19] P. Painlevé, Leçons sur la théorie analytique des équations différentielles (Leçons de Stockholm, delivered in 1895), Hermann, Paris (1897). Reprinted in Œuvres de Paul Painlevé, vol. I, Éditions du CNRS, Paris (1973). [20] A. Ramani, B. Grammaticos, T. Tamizhmani, K. M. Tamizhmani, The road to the discrete analogue of the Painleve property: Nevanlinna meets singularity confinement. Computers & Mathematics with Applications 45, 10011012 (2003). [21] Yu. B. Suris, The Problem of Integrable Discretization: Hamiltonian Approach, Progress in Mathematics, Vol. 219. Basel: Birkhäuser, 2003. [22] P. Tempesta, Integrable maps from Galois differential algebras, Borel transforms and number sequences, Journal of Differential Equations, 255, 2981-2995 (2013). [23] T. Tsuda, Universal character and q-difference Painlevé equations. Mathematische Annalen 345, 395-415 (2009). | |
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