An introduction to WKB analysis II

The Stokes geometry associated with a higher order linear differential equation is quite different from that of the second　order equation.
Ordinary turning points are not enough to describe the complete Stokes geometry.
We need a new object that is called a virtual turning point([BNR],[AKT]).
On the Stokes geometry, each Stokes curve consists of solid line portions and dotted line portions. The solid line portions denote that
the Stokes phenomena really occur and the dotted line portions denote that the Stokes phenomena never occur.
Aoki-Kawai-Takei introduced an algorithm to determine solid or dotted line portions of Stokes curves. The principal aim of this talk is an improvement of the algorithm [AKT] so
that may be applicable to the Stokes geometry that has the geometrical degeneration between Stokes curves.
This is a joint work with N.Honda.