Uniform foliation associated with the hamiltonian system ℋ n
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 20 (1993) no. 1, pp. 1-60. 
@article{ASNSP_1993_4_20_1_1_0,
     author = {Kimura, Hironobu},
     title = {Uniform foliation associated with the hamiltonian system $\mathcal {H}_n$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {1--60},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 20},
     number = {1},
     year = {1993},
     mrnumber = {1215998},
     zbl = {0774.34007},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1993_4_20_1_1_0/}
}
TY  - JOUR
AU  - Kimura, Hironobu
TI  - Uniform foliation associated with the hamiltonian system $\mathcal {H}_n$
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1993
SP  - 1
EP  - 60
VL  - 20
IS  - 1
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1993_4_20_1_1_0/
LA  - en
ID  - ASNSP_1993_4_20_1_1_0
ER  - 
%0 Journal Article
%A Kimura, Hironobu
%T Uniform foliation associated with the hamiltonian system $\mathcal {H}_n$
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1993
%P 1-60
%V 20
%N 1
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1993_4_20_1_1_0/
%G en
%F ASNSP_1993_4_20_1_1_0
Kimura, Hironobu. Uniform foliation associated with the hamiltonian system $\mathcal {H}_n$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 20 (1993) no. 1, pp. 1-60. http://archive.numdam.org/item/ASNSP_1993_4_20_1_1_0/

[AKF] P. Appell - J. Kampé De Fériet, Fonctions hypergéométriques et hypersphériqiues, Gauthier Villars, Paris, 1926. | JFM

[Bout] P. Boutroux, Recherches sur les transcendantes de M. Painlevé et l' étude asymptotique des équations différentielles du second ordre, Ann. Sci. Éeole Norm. Sup., (3) 30 (1913), 255-375; (3) 31 (1914), 99-159. | JFM | Numdam | MR

[Bur] F.J. Bureau, Équations différentielles du second ordre en Y et du second degré en dont l'integrale générale est à points critiques fixes, ibid., 91 (1972), 163-281. | MR | Zbl

[Chaz] J. Chazy, Sur les équations différentielles du troisième ordre et d'ordre supérieur dont l'intégrale a ses points critiques fixes, Acta. Math., 34 (1911), 317-385. | JFM

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

[Gamb] B. Gambier, Sur les équations différentielles du second ordre et du premier degré dont l'intégral générale est à points critiques fixes, Acta. Math. 33 (1910), 1-55. | JFM

[Gar1] R. Garnier, Sur des équations différentielles du troisiéme ordre dont l'intégrale générale est uniforme et sur une classe d'équations nouvelles d'ordre supérieur dont l'intégrale générale a ses point critiques fixes, Ann. Sci. Éeole Norm. Sup., 29 (1912), 1-126. | JFM | Numdam | MR

[Gar2] R. Garnier, Etude de l'intégrale générale de l'équation VI de M. Painlevé, Ann. Sci. Éeole Norm. Sup., (3) série, 34 (1917), 239-353. | JFM | Numdam | MR

[Gar3] R. Garnier, Contribution à l'étude des solutions de l'équation (V) de Painlevé, J. Math. Pures Appl., 46 (1968), 353-413. | MR | Zbl

[Gel] I.M. Gelfand, General theory of hypergeometric functions, Soviet Math. Dokl., 33 (1986), 573-577. | MR | Zbl

[Hirz] F. Hirzebruch, Uber eine Klasse von einfach zusammenhngenden Komplexen Mannigfaltigkeiten, Math. Ann., 124 (1951), 77-86. | MR | Zbl

[Inc] E.L. Ince, Ordinary Differential Equations, Dover, 1956. | MR | Zbl

[Iws] K. Iwasaki, Moduli and deformation for Fuchsian projective connections on a Riemann surface, Univ. Tokyo preprint 89-16. | MR

[Jimb] M. Jimbo, Monodromy problem and the boundary condition for some Painlevé equations, Publ. Res. Inst. Math. Sci., 18 (1982), 1137-1161. | MR | Zbl

[JMU] M. Jimbo - T. Miwa - K. Ueno, Monodromy preserving deformation of linear ordinary differential equations with rational coefficients, I, Phys. D, 2 (1981), 306-352. | MR

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

[KimH1] H. Kimura, On the isomonodromic deformation of linear ordinary differential equations of the third order, Proc. Japan Acad., 57 (1981), 446-449. | Zbl

[KimH2] H. Kimura, The construction of a general solution of a Hamiltonian system with regular type singularity and its application to Painlevé equations, Ann. Mat. Pura Appl., 134 (1983), 363-392. | MR | Zbl

[KimH3] 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

[KimH4] H. Kimura, Generalization of Hirzebruch surface to 2n-dimensional manifold, (preprint).

[KimH5] H. Kimura, Symmetries of the Garnier system and of the associated polynomial Hamiltonian system, preprint, Tokyo Univ., (1990). | MR

[KimH6] H. Kimura, Symmetries of the Hamiltonian system Hn and of the hypergeometric equation for FD, preprint, Tokyo Univ., (1990). | MR

[KO1] H. Kimura - K. Okamoto, On the isomonodromic deformation of linear ordinary differential equations of higher order, Funkcial. Ekvac., 26 (1983), 37-50. | MR | Zbl

[KO2] H. Kimura - K. Okamoto, On the polynomial Hamiltonian structure of the Garnier systems, J. Math. Pures Appl., 63 (1984), 129-146. | MR | Zbl

[Kod] K. Kodaira, Complex manifolds and deformation of complex analytic structures, Lecture Note, Tokyo Univ. (in Japanese).

[MTW] B.M. Maccoy - C.A. Tracy - T.T. Wu, Painlevé functions of the third kind, J. Math. Phys., 18 (1977), 1058-1092. | MR | Zbl

[Malg] B. Malgrange, Sur les déformation isomonodromiques, I, Singularités régulierès, séminaire E.N.S. Birkhäuser, 1982. | MR | Zbl

[Mal] J. Malmquist, Sur les équations différentielles du second ordre dont l'intégrale générale a ses points critiques fixes, Ark. Mat. Astr. Fys., 17 (1922-23), 1-89. | JFM

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

[Mur1] Y Murata, Rational solutions of the second and the fourth Painlevé equations, Funkcial. Ekvac., 28 (1985), 1-32. | MR | Zbl

[Nis.2] K. Nishioka, A note on the transcendency of Painlevé first transcendent, Nagoya Math. J., 109 (1988), 63-67. | MR | Zbl

[Okm.1] K. Okamoto, Sur les feuilletages associé aux équations du second ordre à points critiques fixes de P. Painlevé, Japan J. Math., 5 (1979), 1-79. | MR | Zbl

[Okm.2] K. Okamoto, Isomonodromic deformation and Painlevé equations and the Gamier system, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 33 (1986), 575-618. | MR | Zbl

[Okm.3] K. Okamoto, Studies on the Painlevé equations, I, Ann. Mat. Pura Appl., 146 (1987), 337-381; II, Japan J. Math., 13 (1987), 47-76; III, Math. Ann., 275 (1986), 221-256; IV, Funkcial. Ekvac., 30 (1987), 305-332. | MR

[OK] H. Kimura - K. Okamoto, On particular solutions of Garnier systems and the hypergeometric functions of several variables, Quart. J. Math., 37 (1986), 61-80. | MR | Zbl

[Pain] P. Painlevé, Œuvres t. I, II, III, CNRS, Paris, 1976.

[R] B.L. Reinhart, Differential Geometry of Foliations, Springer-Verlag, 1983. | MR | Zbl

[Schl] L. Schlesinger, Über eine Klasse von differentialsystemen beliebliger Ordnung mit festen Kritischer Punkten, J. für Math., 141 (1912), 96-145. | JFM

[Shim.1] S. Shimomura, Series expansions of Painlevé transcendents in the neighbourhood of a fixed singular points, Funkcial. Ekvac., 25 (1982), 185-197. | MR | Zbl

[Shim.2] S. Shimomura, Supplement to "Series expansions of Painlevé transcendents in the neighbourhood of a fixed singular points", Funkcial. Ekvac., 25 (1982), 363-371. | MR | Zbl

[Tak.1] K. Takano, A 2-parameter family of solutions of Painlevé equation (V) near the point at infinity, Funkcial. Ekvac., 26 (1983), 79-113. | MR | Zbl

[Tak.2] K. Takano, Reduction for Painlevé equations at the fixed singular points of the first kind, Funkcial. Ekvac., 29 (1986), 99-119. | MR | Zbl

[Ume.1] H. Umemura, Birational automorphism groups and differential equations, (colloque franco-japonais) Publications IRMA, (1989). | MR

[Ume.2] H. Umemura, On the irreducibility of the first differential equation of Painlevé, Algebraic geometry and Commutative algebra in honor of Masayoshi Nagata, (1987), 101-119. | MR | Zbl

[Ume.3] H. Umemura, On the second proof of the irreducibility of the first differential equation of Painlevé, Kumamoto Univ. preprint (1988). | MR

[YIKS] M. Yoshida - K. Iwasaki - H. Kimura - S. Shimomura, Gauss to Painlevé, Vieweg Verlag, Wiesbaden, 1990. | Zbl

[YosM] M. Yoshida, Fuchsian differential equations, Vieweg Verlag, Wiesbaden, 1987. | MR | Zbl

[YosS] S. Yoshida, A 2-parameter family of solutions of Painlevé equations (I)-(V) at an irregular singular point, Funkcial. Ekvac., 28 (1985), 233-248. | MR | Zbl