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In our previous work, a unified description as polynomial Hamiltonian systems was established for a broad class of the Schlesinger systems including the sixth Painleve equation and Garnier systems.
R. Fuchs, Über lineare homogene Differentialgleichungen zweiter Ordnung mit drei im Endlichen gelegenen wesentlich singulären Stellen,
1907
Earlier work this paper cites.
R. Garnier, 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 a ses points critiques fixes,
1912
Earlier work this paper cites.
L. Schlesinger, Über eine Klasse von Differentialsystemen beliebiger Ordnung mit festen kritischen Punkten,
1912
Earlier work this paper cites.
J. Malmquist, Sur les équations différentielles du second ordre dont l’intégrale générale a ses points critiques fixes,
1922
Earlier work this paper cites.
P. Appell and J. Kampé de Fériet,
1926
Cited alongside, same era.
H. Kimura and K. Okamoto, On the polynomial Hamiltonian structure of the Garnier system,
1984
Cited alongside, same era.
K. Okamoto and H. Kimura, On particular solutions of the Garnier systems and the hypergeometric functions of several variables,
1986
Cited alongside, same era.
K. Okamoto, Studies on the Painlevé equations. I. Sixth Painlevé equation
1987
Cited alongside, same era.
G. Lauricella, Sulle funzioni ipergeometriche a più variabili,
Cited in the paper.
T. Suzuki, A particular solution of a Painlevé system in terms of the hypergeometric function
Cited in the paper.
J. Thomae, Ueber die höheren hypergeometrischen Reihen, insbesondere über die Reihe:
Cited in the paper.
Cited in the paper.
K. Aomoto and M. Kita,
1994
Later among the works it cites.
M. Yoshida,
1997
Later among the works it cites.
T. Tsuda, Universal characters and an extension of the KP hierarchy,
2004
Later among the works it cites.
B. Dubrovin and M. Mazzocco, On the reductions and classical solutions of the Schlesinger equations, in: D. Bertrand, B. Enriquez, C. Mitschi, C. Sabbah and R. Schäfke (Eds.),
2007
Later among the works it cites.
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