Birational canonical transformations and classical solutions of the sixth Painlevé equation
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 27 (1998) no. 3-4, pp. 379-425. 
@article{ASNSP_1998_4_27_3-4_379_0,
     author = {Watanabe, Humihiko},
     title = {Birational canonical transformations and classical solutions of the sixth {Painlev\'e} equation},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {379--425},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 27},
     number = {3-4},
     year = {1998},
     mrnumber = {1678014},
     zbl = {0933.34095},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1998_4_27_3-4_379_0/}
}
TY  - JOUR
AU  - Watanabe, Humihiko
TI  - Birational canonical transformations and classical solutions of the sixth Painlevé equation
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1998
SP  - 379
EP  - 425
VL  - 27
IS  - 3-4
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1998_4_27_3-4_379_0/
LA  - en
ID  - ASNSP_1998_4_27_3-4_379_0
ER  - 
%0 Journal Article
%A Watanabe, Humihiko
%T Birational canonical transformations and classical solutions of the sixth Painlevé equation
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1998
%P 379-425
%V 27
%N 3-4
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1998_4_27_3-4_379_0/
%G en
%F ASNSP_1998_4_27_3-4_379_0
Watanabe, Humihiko. Birational canonical transformations and classical solutions of the sixth Painlevé equation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 27 (1998) no. 3-4, pp. 379-425. http://www.numdam.org/item/ASNSP_1998_4_27_3-4_379_0/

[1] N. Bourbaki, "Groupes et algèbres de Lie", Chapitres 4, 5, et 6, Masson, Paris, 1981. | MR | Zbl

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

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

[4] K. Okamoto, Studies on the Painlevé equations I, Sixth Painlevé equation PVI, Ann. Mat. Pura Appl. 146 (1987), 337-381. | MR | Zbl

[5] P. Painlevé, Sur les équations différentielles du second ordre à points critiques fixes, C. R. Acad. Sci. Paris 143 (1906), 1111-1117. | JFM

[6] T. Shioda - K. Takano, On some Hamiltonian structures of Painlevé systems, I, Funkcial. Ekvac. 40 (1997), 271-291. | MR | Zbl

[7] H. Umemura, Birational automorphism groups and differential equations, Nagoya Math. J. 119 (1990), 1-80. | MR | Zbl

[8] H. Umemura, On the irreducibility of the first differential equation of Painlevé, In: "Algebraic Geometry and Commutative Algebra in Honor of Masayoshi NAGATA", Kinokuniya, Tokyo, 1987, pp. 771-789. | MR | Zbl

[9] H. Umemura, Second proof of the irreducibility of first differential equation of Painlevé, Nagoya Math. J. 117 (1990), 125-171. | MR | Zbl

[10] H. Umemura - H. Watanabe, Solutions of the second and fourth Painlevé equations I, Nagoya Math. J. 148 (1997), 151-198. | MR | Zbl

[11] H. Umemura - H. Watanabe, Solutions of the third Painlevé equation I, Nagoya Math. J. 151 (1998), 1-24. | MR | Zbl

[12] H. Watanabe, Solutions of the fifth Painlevé equation I, Hokkaido Math. J. 24 (1995), 231-267. | MR | Zbl

[13] H. Watanabe, On the defining variety and birational canonical transformations of the fourth Painlevé equation, to appear in Funkcial. Ekvac. | MR | Zbl

[14] H. Watanabe, Defining variety and birational canonical transformations of the fifth Painlevé equation, to appear in Analysis. | MR | Zbl

[15] H. Watanabe, On the root system of type D4 and thefour-dimensional regular trisoctahedron, preprint.