Geometric properties of the Riemann surfaces associated with the Noumi-Yamada systems with a large parameter

Takashi AOKI and Naofumi HONDA
Source: J. Math. Soc. Japan Volume 63, Number 4 (2011), 1085-1119.

Abstract

The system of algebraic equations for the leading terms of formal solutions to the Noumi-Yamada systems with a large parameter is studied. A formula which gives the number of solutions outside of turning points is established. The number of turning points of the first kind is also given.

First Page:
Primary Subjects: 34M55, 34M60
Secondary Subjects: 34E20, 34M25
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1319721136
Digital Object Identifier: doi:10.2969/jmsj/06341085
Zentralblatt MATH identifier: 05992428
Mathematical Reviews number (MathSciNet): MR2855808

References

T. Aoki and N. Honda, Regular sequence associated with the Noumi-Yamada equations with a large parameter, Algebraic Analysis of Differential Equations, Springer, 2008, pp.,45–53.
Mathematical Reviews (MathSciNet): MR2758897
Zentralblatt MATH: 1162.34072
T. Aoki, N. Honda and Y. Umeta, On the number of the turning points of the second kind of the Noumi-Yamada system, RIMS Kôkyûroku Bessatsu, to appear.
T. Suwa, Dual class of a subvariety, Tokyo J. Math., 23 (2000), 51–68.
Mathematical Reviews (MathSciNet): MR1763504
Digital Object Identifier: doi:10.3836/tjm/1255958807
Project Euclid: euclid.tjm/1255958807
Zentralblatt MATH: 0971.32005
Y. Takei, Toward the exact WKB analysis for higher-order Painlevé equations – The case of Noumi-Yamada Systems –, Publ. Res. Inst. Math. Sci., 40 (2004), 709–730.
Mathematical Reviews (MathSciNet): MR2074698
Digital Object Identifier: doi:10.2977/prims/1145475490
M. Noumi and Y. Yamada, Higher order Painlevé equations of type $A_l^{(1)}$, Funkcial Ekvac., 41 (1998), 483–503.
Mathematical Reviews (MathSciNet): MR1676885
M. Noumi and Y. Yamada, Symmetry in Painlevé equations, In: Toward the Exact WKB Analysis of Differential Equations, (eds. C. J. Howls, T. Kawai and Y. Takei), Linear or Non-Linear, Kyoto Univ. Press, 2000, pp.,245–260.
Mathematical Reviews (MathSciNet): MR1770297