Birational canonical transformations and classical solutions of the sixth Painlevé equation

Humihiko Watanabe

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 27, Issue: 3-4, page 379-425
  • ISSN: 0391-173X

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Watanabe, Humihiko. "Birational canonical transformations and classical solutions of the sixth Painlevé equation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 27.3-4 (1998): 379-425. <http://eudml.org/doc/84362>.

@article{Watanabe1998,
author = {Watanabe, Humihiko},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {sixth Painlevé equation; birational canonical transformations; affine Weyl group; symmetry; Hamiltonian; JFM 37.0341.04},
language = {eng},
number = {3-4},
pages = {379-425},
publisher = {Scuola normale superiore},
title = {Birational canonical transformations and classical solutions of the sixth Painlevé equation},
url = {http://eudml.org/doc/84362},
volume = {27},
year = {1998},
}

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
PB - Scuola normale superiore
VL - 27
IS - 3-4
SP - 379
EP - 425
LA - eng
KW - sixth Painlevé equation; birational canonical transformations; affine Weyl group; symmetry; Hamiltonian; JFM 37.0341.04
UR - http://eudml.org/doc/84362
ER -

References

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  1. [1] N. Bourbaki, "Groupes et algèbres de Lie", Chapitres 4, 5, et 6, Masson, Paris, 1981. Zbl0483.22001MR647314
  2. [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. Zbl0426.58017MR614694
  3. [3] K. Okamoto, Isomonodromic deformation and Painlevé equations, and the Garnier system, J. Fac. Sci. Univ. Tokyo Sect. IA Math.33 (1986), 575-618. Zbl0631.34011MR866050
  4. [4] K. Okamoto, Studies on the Painlevé equations I, Sixth Painlevé equation PVI, Ann. Mat. Pura Appl.146 (1987), 337-381. Zbl0637.34019MR916698
  5. [5] P. Painlevé, Sur les équations différentielles du second ordre à points critiques fixes, C. R. Acad. Sci. Paris143 (1906), 1111-1117. Zbl37.0341.04JFM37.0341.04
  6. [6] T. Shioda - K. Takano, On some Hamiltonian structures of Painlevé systems, I, Funkcial. Ekvac.40 (1997), 271-291. Zbl0891.34003MR1480279
  7. [7] H. Umemura, Birational automorphism groups and differential equations, Nagoya Math. J.119 (1990), 1-80. Zbl0714.12009MR1071899
  8. [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. Zbl0704.12007MR977782
  9. [9] H. Umemura, Second proof of the irreducibility of first differential equation of Painlevé, Nagoya Math. J.117 (1990), 125-171. Zbl0688.34006MR1044939
  10. [10] H. Umemura - H. Watanabe, Solutions of the second and fourth Painlevé equations I, Nagoya Math. J.148 (1997), 151-198. Zbl0934.33029MR1492945
  11. [11] H. Umemura - H. Watanabe, Solutions of the third Painlevé equation I, Nagoya Math. J.151 (1998), 1-24. Zbl0917.34004MR1650348
  12. [12] H. Watanabe, Solutions of the fifth Painlevé equation I, Hokkaido Math. J.24 (1995), 231-267. Zbl0833.34005MR1339823
  13. [13] H. Watanabe, On the defining variety and birational canonical transformations of the fourth Painlevé equation, to appear in Funkcial. Ekvac. Zbl1141.34357MR1709805
  14. [14] H. Watanabe, Defining variety and birational canonical transformations of the fifth Painlevé equation, to appear in Analysis. Zbl0923.34003MR1670675
  15. [15] H. Watanabe, On the root system of type D4 and thefour-dimensional regular trisoctahedron, preprint. 

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