Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 1, pp. 1-17.
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     title = {Painlev\'e property of a degenerate {Garnier} system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Shimomura, Shun. Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 1, pp. 1-17. http://www.numdam.org/item/ASNSP_2000_4_29_1_1_0/

[1] H. Flaschka - A.C. Newell, Monodromy- and spectrum-preserving deformations I, Comm. Math. Phys. 76 (1980), 65-116. | MR | Zbl

[2] R. Fuchs, Über lineare homogene Differentialgleichungen zweiter Ordnung mit drei im Endlichen gelegene wesentlich singulären Stellen, Math. Ann. 63 (1907), 301-321. | JFM | MR

[3] R. Garnier, Sur des équations différentielles du troisième ordre dont l'intégrale générale est uniforme et sur une classe d'équations nouvelles d'ordre supérieur dont l'intégrale générale a ses points critiques fixes, Ann. Sci. École Norm. Sup. 29 (1912), 1-126. | JFM | Numdam | MR

[4] K. Iwasaki - H. Kimura - S. Shimomura - M. Yoshida, "From Gauss to Painlevé, A Modern Theory of Special Functions ", Vieweg, Braunschweig, 1991. | MR | Zbl

[5] M. Jimbo - T. Miwa - K. Ueno, Monodromy preserving deformation of linear ordinary differential equations with rational coefficients, I, - General theory and τ-function -, Phys. D 2 (1981), 306-352.

[6] M. Jimbo - T. Miwa, Monodromy preserving deformation of linear ordinary differential equations with rational coefficients, II, Phys. D 2 (1981), 407-448. | MR

[7] H. Kimura, The degeneration of the two dimensional Garnier system and the polynomial Hamiltonian structure, Ann. Mat. Pura Appl. 155 (1989), 25-74. | MR | Zbl

[8] H. Kimura - K. Okamoto, On the polynomial Hamiltonian structure of the Garnier system, J. Math. Pures Appl. 63 (1984), 129-146. | MR | Zbl

[9] B. Malgrange, "Sur les déformations isomonodromiques, I: Singularités régulières", Séminaire de l'École Norm. Sup., Birkhäuser, 1982. | MR | Zbl

[10] T. Miwa, Painlevé property of monodromy preserving deformation equations and the analyticity of τ -functions, Publ. Res. Inst. Math. Sci. 17 (1981), 703-721. | Zbl

[11] M. Noumi - Y. Yamada, Higher order Painlevé equations of type Al (1), Funkcial. Ekvac. 41 (1998), 483-503. | MR | Zbl

[12] M. Noumi - Y. Yamada, private communication.

[13] K. Okamoto, Isomonodromic deformation and Painleve equations, and the Garnier system, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 33 (1986), 575-618. | MR | Zbl

[14] L. Schlesinger, Über eine Klasse von Differentialsystemen beliebiger Ordnung mit festen kritischen Punkten, J. Reine Angew. Math. 141 (1912), 96-145. | JFM

[15] K. Ueno, Monodromy preserving deformation of linear differential equations with irregular singular points, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980), 97-102. | MR | Zbl