ON THE CLASSIFICATION OF SINGULAR AUTOMORPHIC DIFFERENTIAL EQUATIONS AND FLOW S ON THE RIEMANN SPHERE

Authors

  • K. F. KUIKEN Polytechnic University, Six Metrotech Center, Brooklyn, New York 11201, U. S. A
  • J. T. MASTERSON Seton Hall University, 400 South Orange Avenue, South Orange, New Jersey 07079, U. S. A.

DOI:

https://doi.org/10.5556/j.tkjm.26.1995.4373

Keywords:

Automorphic differential equations, bimeromorphic deformations of Kleinian groups, fluid flows

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.

References

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H. Kober, Dictionary of Conformal Representations, Dover Publications, New York, 1952

K. Kuiken and J. T. Masterson, "On Global Solutions and Monodromy Groups of Differential Equations Having at Least Two Singularities on the Riemann Sphere," Indagationes mathematicae, 90 (1987), 301-312.

A. I. Markushevich, Theory of Functions of a Complex Variable, Chelsea Publishing Company, New York, 1977.

W. S. Massey, Algebraic Topology: An Introduction, Springer-Verlag, New York, 1967.

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Published

1995-03-01

How to Cite

KUIKEN, K. F. ., & MASTERSON , J. T. . (1995). ON THE CLASSIFICATION OF SINGULAR AUTOMORPHIC DIFFERENTIAL EQUATIONS AND FLOW S ON THE RIEMANN SPHERE. Tamkang Journal of Mathematics, 26(1), 13–19. https://doi.org/10.5556/j.tkjm.26.1995.4373

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Section

Papers