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monodromy groups


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1: 15.17 Mathematical Applications
§15.17(v) Monodromy Groups
By considering, as a group, all analytic transformations of a basis of solutions under analytic continuation around all paths on the Riemann sheet, we obtain the monodromy group. These monodromy groups are finite iff the solutions of Riemann’s differential equation are all algebraic. …
2: 31.16 Mathematical Applications
§31.16(i) Uniformization Problem for Heun’s Equation
It describes the monodromy group of Heun’s equation for specific values of the accessory parameter. …
3: Bibliography D
  • B. Dubrovin and M. Mazzocco (2000) Monodromy of certain Painlevé-VI transcendents and reflection groups. Invent. Math. 141 (1), pp. 55–147.
  • 4: Bibliography
  • V. I. Arnol’d, S. M. Guseĭn-Zade, and A. N. Varchenko (1988) Singularities of Differentiable Maps. Vol. II. Birkhäuser, Boston-Berlin.
  • V. I. Arnol’d (1972) Normal forms of functions near degenerate critical points, the Weyl groups A k , D k , E k and Lagrangian singularities. Funkcional. Anal. i Priložen. 6 (4), pp. 3–25 (Russian).
  • R. A. Askey, T. H. Koornwinder, and W. Schempp (Eds.) (1984) Special Functions: Group Theoretical Aspects and Applications. D. Reidel Publishing Co., Dordrecht.