ON THE CLASSIFICATION OF SINGULAR AUTOMORPHIC DIFFERENTIAL EQUATIONS AND FLOW S ON THE RIEMANN SPHERE
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Abstract
In this paper, parameterizations are constructed for spaces of automor phic second order differential equations on certam subsets of $\hat C$. These equations have coefficients with a countable number of regular singular points on fundamen tal domains for bimeromorphic deformations of Kleiman groups. The equations considered are generalizations of classically-considered equations, including the hy pergeometric and Heun's equations, or have singular points on fam1hes of curves, including lines, conic sections, Joukowski airfoils or biconformal images of these curves. Global fluid flows associate with these equations are constructed and classified.
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