Stokes curves of second order Fuchsian dfferential equations on the Riemann sphere with a large parameter form sphere graphs, which are called Stokes graphs. Topological classiﬁcation of Stokes graphs are given for the case where equations have ﬁve regular singular points. It is proved that there are exactly 25 degree sequences of sphere triangulations associated with Stokes graphs under suitable generic conditions.
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Takashi Aoki, Takayuki Iizuka, Classiﬁcation of Stokes Graphs of Second Order Fuchsian Diﬀerential Equations of Genus Two. Publ. Res. Inst. Math. Sci. 43 (2007), no. 1, pp. 241–276DOI 10.2977/PRIMS/1199403816