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.

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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)

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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