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.
"Geometric properties of the Riemann surfaces associated with the Noumi-Yamada systems with a large parameter." J. Math. Soc. Japan 63 (4) 1085 - 1119, October, 2011. https://doi.org/10.2969/jmsj/06341085