ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 30, 34 Misaki, Norihiro, College of Science and Technology, Nihon University, Japan Application of Apparent Monodromy Groups Let S_{α} be a set of solutions of a LDE containing a parameter α, which is fundamental at a value of α. S_{α} often turns nonfundamental when the monodromy group with respect to it is reducible. So the reducibility has been got as only necessary condition and special argument must have been held whether it is also sufficient. In 1993, the author introduced the concept of apparent monodromy groups and showed that the condition is always sufficient if the coefficients of LDE and S_{α} depend holomorphically on α. In this poster, application of apparent monodromy groups is shown in the case of Pochhammer’s equation.