MR2547101
Hiroyuki KAWAMUKO
Hiroyuki KAWAMUKO
On the Garnier System of Half-Integer Type in Two Variables
Funkcialaj Ekvacioj. Serio Internacia
52
2009
181--201
http://fe.math.kobe-u.ac.jp/FE/FullPapers/52-2/52_181.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2547101
In [5], Kimura proposed degenerate Garnier systems in two variables. In this paper, we propose Hamiltonian systems which are considered as degenerate cases of Kimura's degenerate Garnier systems.
Garnier system, Monodromy preserving deformation.
34M55.
52-181
2009
On the Garnier System of Half-Integer Type in Two Variables
Hiroyuki KAWAMUKO
Hiroyuki KAWAMUKO
1
Fuchs, R.
Uber lineare homogene Differentialgleichungen zweiter Ordnung mit drei im Endlichen gelegene wesentlich singulären Stellen
Math. Ann.
63
1907
301-321
MR1511408
2
Garnier, R.
Sur des équations différentielles du troisième ordre dont l'intégrale générale est uniforme et sur une classe d'équations nouvelles d'ordre supérieur dont l'intégrale générale à ses points critiques fixes
Ann. Sci. École Norm. Sup. (3)
29
1912
1-126
MR1509146
3
Kawamuko, H.
Rational solutions of the fourth Painlevé equation in two variables
Funkcial. Ekvac.
46
2003
1-21
MR1996291
1996291
4
Kawamuko, H., On Special solutions of the degenerate Garnier system $(3,2)$ and $G(5/2,1,1)$, in preparation
5
Kimura, H.
The degeneration of the two dimensional Garnier system and the polynomial Hamiltonian structure
Ann. Mat. Pura Appl. (4)
155
1989
25-74
MR1042827
6
Ohyama, Y.; Okumura, S., Complete coalescent diagram of the Painlevé equations, math.CA/0601614
7
Ohyama, Y.; Kawamuko, H.; Sakai, H.; Okamoto, K.
Studies on the Painlevé Equations V
J. Math. Sci. Univ. Tokyo
13
2006
145-204
MR2277519
8
Okamoto, K.
Isomonodromic deformation and Painlevé equations, and the Garnier system
J. Fac. Sci. Univ. Tokyo Sect. IA, Math.
33
1986
575-618
MR0866050