Birational Canonical Transformations and Classical Solutions of the Sixth Painlevé Equation

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Volumn 27, Issue 3-4, 1998, Pages 379-425

  Watanabe, Humihiko ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000180238     PISSN: 0391173X     EISSN: 20362145     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

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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.
3. K . OKAMOTO, IsomonodromicdeformationandPainlevéequations, andtheGarniersystem, J. Fac. Sci. Univ. Tokyo Sect. lA Math. 33 (1986), 575-618.
4. K . OKAMOTO, Studies on the Painlevé equations I, Sixth Painlevé equation Pyj, Ann. Mat. Pura Appi. 146 (1987), 337-381.
5. P. PAINLEVÉ, Sur les équations différentielles du second ordre à points critiques fixes, C. R. Acad. Sci. Paris 143 (1906), 1111-1117.
6. T . SHIODA - K . TAKANO, On some Hamiltonian structures of Painlevé systems, /, Funkcial. Ekvac. 40(1997), 271-291.
7. H . UMEMURA, Birational automorphism groups and differential equations, Nagoya Math. J. 119(1990), 1-80.
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.
9. H . UMEMURA, Second proof of the irreducibility of first differential equation of Painlevé, Nagoya Math. J. 117 (1990), 125-171.
10. H . UMEMURA - H . WATANABE. Solutions of the second and fourth Painlevé equations I, Nagoya Math. J. 148 (1997), 151-198.
11. H . UMEMURA - H. WATANABE, Solutions of the third Painlevé equation J, Nagoya Math. J. 151 (1998), 1-24.
12. H . WATANABE, Solutions of the fifth Painlevé equation J, Hokkaido Math. J . 24 (1995), 231-267.
13. H . WATANABE, On the defining variety and birational canonical transformations of the fourth Painlevé equation, to appear in Funkcial. Ekvac.
14. H . WATANABE, Defining variety and birational canonical transformations of the fifth Painlevé equation, to appear in Analysis.
15. H . WATANABE, On the root system of type D4 and the four-dimensional regular trisoctahedron, preprint.