Isomonodromy for the Degenerate Fifth Painlev e Equation
| dc.contributor.author | Acosta-Humánez, Primitivo B. | |
| dc.contributor.author | Van Der Put, Marius | |
| dc.contributor.author | Top, Jaap | |
| dc.date.accessioned | 2018-03-05T13:59:54Z | |
| dc.date.available | 2018-03-05T13:59:54Z | |
| dc.date.issued | 2017-05-09 | |
| dc.description.abstract | This is a sequel to papers by the last two authors making the Riemann{Hilbert correspondence and isomonodromy explicit. For the degenerate fifth Painlev e equation, the moduli spaces for connections and for monodromy are explicitly computed. It is proven that the extended Riemann{Hilbert morphism is an isomorphism. As a consequence these equations have the Painlev e property and the Okamoto{Painlev e space is identified with a moduli space of connections. Using MAPLE computations, one obtains formulas for the degenerate fifth Painlev e equation, for the B acklund transformations. | eng |
| dc.identifier.issn | 11317787 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.12442/1773 | |
| dc.language.iso | eng | spa |
| dc.publisher | Eusko Jaurlaritza Gobierno Vasco | spa |
| dc.rights.accessrights | info:eu-repo/semantics/openAccess | |
| dc.source | Revista SIGMA | spa |
| dc.source | Vol. 13, No. 029 (2017) | spa |
| dc.source.uri | https://www.emis.de/journals/SIGMA/2017/029/sigma17-029.pdf | |
| dc.subject | Moduli space for linear connections | eng |
| dc.subject | Irregular singularities | eng |
| dc.subject | Stokes matrices | eng |
| dc.subject | Monodromy spaces | eng |
| dc.subject | Isomonodromic deformations | eng |
| dc.subject | Painlev´e equations | eng |
| dc.title | Isomonodromy for the Degenerate Fifth Painlev e Equation | eng |
| dc.type | article | spa |
| dcterms.references | Chekhov L., Mazzocco M., Rubtsov V., Painlev´e monodromy manifolds, decorated character varieties and cluster algebras, Int. Math. Res. Not., to appear, arXiv:1511.03851 | eng |
| dcterms.references | Fokas A.S., Its A.R., Kapaev A.A., Novokshenov V.Yu., Painlev´e transcendents. The Riemann–Hilbert approach, Mathematical Surveys and Monographs, Vol. 128, Amer. Math. Soc., Providence, RI, 2006 | eng |
| dcterms.references | Gromak V.I., On the theory of Painlev´e’s equations, Differential Equations 11 (1975), 285–287 | eng |
| dcterms.references | Inaba M., Moduli of parabolic connections on curves and the Riemann–Hilbert correspondence, J. Algebraic Geom. 22 (2013), 407–480, math.AG/060200. | eng |
| dcterms.references | Inaba M., Iwasaki K., Saito M.-H., Dynamics of the sixth Painlev´e equation, in Th´eories asymptotiques et ´equations de Painlev´e, S´emin. Congr., Vol. 14, Soc. Math. France, Paris, 2006, 103–167 | eng |
| dcterms.references | Inaba M., Iwasaki K., Saito M.-H., Moduli of stable parabolic connections, Riemann–Hilbert correspondence and geometry of Painlev´e equation of type VI. I, Publ. Res. Inst. Math. Sci. 42 (2006), 987–1089, math.AG/0309342. | eng |
| dcterms.references | Inaba M., Iwasaki K., Saito M.-H., Moduli of stable parabolic connections, Riemann–Hilbert correspondence and geometry of Painlev´e equation of type VI. II, in Moduli Spaces and Arithmetic Geometry, Adv. Stud. Pure Math., Vol. 45, Math. Soc. Japan, Tokyo, 2006, 387–432, math.AG/0605025 | eng |
| dcterms.references | Jimbo M., Miwa T., Ueno K., Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I. General theory and τ -function, Phys. D 2 (1981), 306–352 | eng |
| dcterms.references | Jimbo M., Miwa T., Monodromy preserving deformation of linear ordinary dif ferential equations with rational coefficients. II, Phys. D 2 (1981), 407–448 | eng |
| dcterms.references | Ohyama Y., Kawamuko H., Sakai H., Okamoto K., Studies on the Painlev´e equations. V. Third Painlev´e equations of special type PIII(D7) and PIII(D8), J. Math. Sci. Univ. Tokyo 13 (2006), 145–204 | eng |
| dcterms.references | Ohyama Y., Okumura S., R. Fuchs’ problem of the Painlev´e equations from the first to the fifth, in Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, Contemp. Math., Vol. 593, Amer. Math. Soc., Providence, RI, 2013, 163–178, math.CA/0512243 | eng |
| dcterms.references | Okamoto K., Sur les feuilletages associ´es aux ´equations du second ordre `a points critiques fixes de P. Painlev´e. Espaces des conditions initiales, Japan. J. Math. 5 (1979), 1–79 | eng |
| dcterms.references | Okamoto K., Isomonodromic deformation and Painlev´e equations, and the Garnier system, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 33 (1986), 575–618 | eng |
| dcterms.references | Okamoto K., Studies on the Painlev´e equations. III. Second and fourth Painlev´e equations, PII and PIV, Math. Ann. 275 (1986), 221–255 | eng |
| dcterms.references | Okamoto K., Studies on the Painlev´e equations. IV. Third Painlev´e equation PIII, Funkcial. Ekvac. 30 (1987), 305–332 | eng |
| dcterms.references | Okamoto K., The Hamiltonians associated to the Painlev´e equations, in The Painlev´e property, CRM Ser. Math. Phys., Springer, New York, 1999, 735–787. | eng |
| dcterms.references | van der Put M., Families of linear dif ferential equations related to the second Painlev´e equation, in Algebraic Methods in Dynamical Systems, Banach Center Publ., Vol. 94, Polish Acad. Sci. Inst. Math., Warsaw, 2011, 247–262 | eng |
| dcterms.references | van der Put M., Families of linear differential equations and the Painlev´e equations, in Geometric and Differential Galois Theories, S´emin. Congr., Vol. 27, Soc. Math. France, Paris, 2013, 207–224. | eng |
| dcterms.references | van der Put M., Saito M.-H., Moduli spaces for linear differential equations and the Painlev´e equations, Ann. Inst. Fourier (Grenoble) 59 (2009), 2611–2667, arXiv:0902.1702. | eng |
| dcterms.references | van der Put M., Singer M.F., Galois theory of linear differential equations, Grundlehren der Mathematischen Wissenschaften, Vol. 328, Springer-Verlag, Berlin, 2003. | eng |
| dcterms.references | van der Put M., Top J., A Riemann–Hilbert approach to Painlev´e IV, J. Nonlinear Math. Phys. 20 (2013), suppl. 1, 165–177, arXiv:1207.4335. | eng |
| dcterms.references | van der Put M., Top J., Geometric aspects of the Painlev´e equations PIII(D6) and PIII(D7), SIGMA 10 (2014), 050, 24 pages, arXiv:1207.4023. | eng |
| dcterms.references | Saito M.-H., Takebe T., Classification of Okamoto–Painlev´e pairs, Kobe J. Math. 19 (2002), 21–50, math.AG/0006028. | eng |
| dcterms.references | Saito M.-H., Takebe T., Terajima H., Deformation of Okamoto–Painlev´e pairs and Painlev´e equations, J. Algebraic Geom. 11 (2002), 311–362, math.AG/0006026. | eng |
| dcterms.references | Saito M.-H., Terajima H., Nodal curves and Riccati solutions of Painlev´e equations, J. Math. Kyoto Univ. 44 (2004), 529–568, math.AG/0201225. | eng |
| dcterms.references | Witte N.S., New transformations for Painlev´e’s third transcendent, Proc. Amer. Math. Soc. 132 (2004), 1649–1658, math.CA/0210019. | eng |
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