## Journal of the Mathematical Society of Japan

- J. Math. Soc. Japan
- Volume 63, Number 4 (2011), 1085-1435

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

Takashi AOKI and Naofumi HONDA

#### 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: 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.