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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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.

Article information

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

Dates
First available in Project Euclid: 27 October 2011

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

Subjects
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

Keywords
Noumi-Yamada systems Painlevé hierarchy formal solutions

Citation

AOKI, Takashi; HONDA, Naofumi. Geometric properties of the Riemann surfaces associated with the Noumi-Yamada systems with a large parameter. Journal of the Mathematical Society of Japan 63 (2011), no. 4, 1085--1119. doi:10.2969/jmsj/06341085. http://projecteuclid.org/euclid.jmsj/1319721136.


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References

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