Isomonodromy for the Degenerate Fifth Painlev e Equation
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...
- Autores:
-
Acosta-Humánez, Primitivo B.
Van Der Put, Marius
Top, Jaap
- Tipo de recurso:
- Fecha de publicación:
- 2017
- Institución:
- Universidad Simón Bolívar
- Repositorio:
- Repositorio Digital USB
- Idioma:
- eng
- OAI Identifier:
- oai:bonga.unisimon.edu.co:20.500.12442/1773
- Acceso en línea:
- http://hdl.handle.net/20.500.12442/1773
- Palabra clave:
- Moduli space for linear connections
Irregular singularities
Stokes matrices
Monodromy spaces
Isomonodromic deformations
Painlev´e equations
- Rights
- License
- http://purl.org/coar/access_right/c_abf2
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Isomonodromy for the Degenerate Fifth Painlev e Equation |
| title |
Isomonodromy for the Degenerate Fifth Painlev e Equation |
| spellingShingle |
Isomonodromy for the Degenerate Fifth Painlev e Equation Moduli space for linear connections Irregular singularities Stokes matrices Monodromy spaces Isomonodromic deformations Painlev´e equations |
| title_short |
Isomonodromy for the Degenerate Fifth Painlev e Equation |
| title_full |
Isomonodromy for the Degenerate Fifth Painlev e Equation |
| title_fullStr |
Isomonodromy for the Degenerate Fifth Painlev e Equation |
| title_full_unstemmed |
Isomonodromy for the Degenerate Fifth Painlev e Equation |
| title_sort |
Isomonodromy for the Degenerate Fifth Painlev e Equation |
| dc.creator.fl_str_mv |
Acosta-Humánez, Primitivo B. Van Der Put, Marius Top, Jaap |
| dc.contributor.author.none.fl_str_mv |
Acosta-Humánez, Primitivo B. Van Der Put, Marius Top, Jaap |
| dc.subject.eng.fl_str_mv |
Moduli space for linear connections Irregular singularities Stokes matrices Monodromy spaces Isomonodromic deformations Painlev´e equations |
| topic |
Moduli space for linear connections Irregular singularities Stokes matrices Monodromy spaces Isomonodromic deformations Painlev´e equations |
| description |
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. |
| publishDate |
2017 |
| dc.date.issued.none.fl_str_mv |
2017-05-09 |
| dc.date.accessioned.none.fl_str_mv |
2018-03-05T13:59:54Z |
| dc.date.available.none.fl_str_mv |
2018-03-05T13:59:54Z |
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article |
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http://purl.org/coar/resource_type/c_6501 |
| dc.identifier.issn.none.fl_str_mv |
11317787 |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/20.500.12442/1773 |
| identifier_str_mv |
11317787 |
| url |
http://hdl.handle.net/20.500.12442/1773 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
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http://purl.org/coar/access_right/c_abf2 |
| dc.publisher.spa.fl_str_mv |
Eusko Jaurlaritza Gobierno Vasco |
| dc.source.spa.fl_str_mv |
Revista SIGMA Vol. 13, No. 029 (2017) |
| institution |
Universidad Simón Bolívar |
| dc.source.uri.none.fl_str_mv |
https://www.emis.de/journals/SIGMA/2017/029/sigma17-029.pdf |
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Acosta-Humánez, Primitivo B.9439add6-3451-4b3f-b187-8b8ba4133fcd-1Van Der Put, Marius5e24ab93-6d99-4b57-873e-4eb0de06a4ea-1Top, Jaapff7e2b03-d42f-44c0-a0c0-bd98cd707fec-12018-03-05T13:59:54Z2018-03-05T13:59:54Z2017-05-0911317787http://hdl.handle.net/20.500.12442/1773This 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.engEusko Jaurlaritza Gobierno VascoRevista SIGMAVol. 13, No. 029 (2017)https://www.emis.de/journals/SIGMA/2017/029/sigma17-029.pdfModuli space for linear connectionsIrregular singularitiesStokes matricesMonodromy spacesIsomonodromic deformationsPainlev´e equationsIsomonodromy for the Degenerate Fifth Painlev e Equationarticlehttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/access_right/c_abf2Chekhov L., Mazzocco M., Rubtsov V., Painlev´e monodromy manifolds, decorated character varieties and cluster algebras, Int. Math. Res. Not., to appear, arXiv:1511.03851Fokas 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, 2006Gromak V.I., On the theory of Painlev´e’s equations, Differential Equations 11 (1975), 285–287Inaba M., Moduli of parabolic connections on curves and the Riemann–Hilbert correspondence, J. Algebraic Geom. 22 (2013), 407–480, math.AG/060200.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, 103–167Inaba 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.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/0605025Jimbo 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), 306–352Jimbo M., Miwa T., Monodromy preserving deformation of linear ordinary dif ferential equations with rational coefficients. II, Phys. D 2 (1981), 407–448Ohyama 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), 145–204Ohyama 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/0512243Okamoto 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), 1–79Okamoto K., Isomonodromic deformation and Painlev´e equations, and the Garnier system, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 33 (1986), 575–618Okamoto K., Studies on the Painlev´e equations. III. Second and fourth Painlev´e equations, PII and PIV, Math. Ann. 275 (1986), 221–255Okamoto K., Studies on the Painlev´e equations. IV. Third Painlev´e equation PIII, Funkcial. Ekvac. 30 (1987), 305–332Okamoto K., The Hamiltonians associated to the Painlev´e equations, in The Painlev´e property, CRM Ser. Math. Phys., Springer, New York, 1999, 735–787.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, 247–262van 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.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.van der Put M., Singer M.F., Galois theory of linear differential equations, Grundlehren der Mathematischen Wissenschaften, Vol. 328, Springer-Verlag, Berlin, 2003.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.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.Saito M.-H., Takebe T., Classification of Okamoto–Painlev´e pairs, Kobe J. Math. 19 (2002), 21–50, math.AG/0006028.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.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.Witte N.S., New transformations for Painlev´e’s third transcendent, Proc. Amer. Math. Soc. 132 (2004), 1649–1658, math.CA/0210019.LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bonga.unisimon.edu.co/bitstreams/728a61a9-6fc4-4251-badb-42a262792ecd/download8a4605be74aa9ea9d79846c1fba20a33MD5220.500.12442/1773oai:bonga.unisimon.edu.co:20.500.12442/17732019-04-11 21:51:41.43metadata.onlyhttps://bonga.unisimon.edu.coDSpace UniSimonbibliotecas@biteca.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 |