Journal of the Mathematical Society of Japan

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

Takashi AOKI and Naofumi HONDA

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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.

Article information

J. Math. Soc. Japan, Volume 63, Number 4 (2011), 1085-1119.

First available in Project Euclid: 27 October 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34M55: Painlevé and other special equations; classification, hierarchies; 34M60: Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20]
Secondary: 34E20: Singular perturbations, turning point theory, WKB methods 34M25: Formal solutions, transform techniques

Noumi-Yamada systems Painlevé hierarchy formal solutions


AOKI, Takashi; HONDA, Naofumi. Geometric properties of the Riemann surfaces associated with the Noumi-Yamada systems with a large parameter. J. Math. Soc. Japan 63 (2011), no. 4, 1085--1119. doi:10.2969/jmsj/06341085.

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