Transformations RS42(3) of the ranks ≤ 4 and algebraic solutions of the sixth Painlevé equation

Communications in Mathematical Physics

Volumn 228, Issue 1, 2002, Pages 151-176

  Andreev, F V ^a,b   Kitaev, A V ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b WESTERN ILLINOIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036019254     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200200653     Document Type: Article

References (15)

1. Hitchin, N.J.: A New Family of Einstein Metrics. In: Manifolds and geometry (Pisa, 1993), Sympos. Math. XXXVI. Cambridge: Cambridge Univ. Press, 1996, pp. 190-222
2. Hitchin, N.J.: Poncelet polygons and the Painlevé transcendents. In: Geometry and Analysis (Bombay, 1992). Bombay: Tata Inst. Fund. Res., 1995, pp. 151-185
3. Dubrovin, B.: Geometry of 2D Topological Field Theories. In: Lect. Notes Math. 1620. Berlin-Heidelberg-New York: Springer-Verlag, 120-348, 1995
4. Dubrovin,B., Mazzocco, M.: Monodromy of Certain Painlevé-VI Transcendents and Reflection Groups. Invent. Math. 141, 55-147 (2000)
5. Mazzocco, M.: Piccard and Chazy Solutions of The Painlevé VI Equation. SISSA Preprint no.89/90/FM, 1998
6. Kitaev, A.V.: Special functions of the isomonodromy type. Acta Appl. Math. 64, no. 1, 1-32(2000)
7. Kitaev, A.V.: Special Functions of the Isomonodromy Type, Rational Transformations of Spectral Parameter, and Algebraic Solutions of the Sixth Painlevé Equation. To appear in Algebra i Analiz (Russian), e-preprint (http://xxx.lanl.gov) nlin. SI/0102020, 1-13, 2000
8. Jimbo, M., Miwa, T: Monodromy preserving deformation of linear ordinary differential equations with rational coefficients II. Physica 2D, 407-448 (1981)
9. VI, Annali Mat. Pura Appl. 146, 337-381 (1987)
10. Umemura, H.: Painlevé equations and classical functions Sūgaku 47, no. 4, 341-359 (1995) (Japanese); English transl. in Sugaku Expositions 11, no. 1, 77-100 (1998)
11. Umemura, H.: Painlevé equations and classical functions Sūgaku 47, no. 4, 341-359 (1995) (Japanese); English transl. in Sugaku Expositions 11, no. 1, 77-100 (1998)
12. Manin, Yu.I.: Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces. American Mathematical Society, Colloquium Publications, Vol. 47, Providence, RI: AMS, 1999
13. 2 (3)-Transformations of Ranks 5 and 6 as the Higher Order Transformations for the Hypergeometric Function. e-preprint (http://xxx.lanl.gov) nlin. SI0012052, 1-20, 2000
14. Jimbo, M.: Monodromy problem and the boundary condition for some Painlevé equations, Publ. RIMS Kyoto Univ. 18, 1137-1161 (1982)
15. Kitaev, A.V.: Non-Schlesinger Deformations of Ordinary Differential Equations with Rational Coefficients, J. Phys. A: Math. Gen. 34, no. 11, 2259-2272 (2001)