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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: 16.23 Mathematical Applications
These equations are frequently solvable in terms of generalized hypergeometric functions, and the monodromy of generalized hypergeometric functions plays an important role in describing properties of the solutions. …
3: 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. …
4: Bibliography J
  • M. Jimbo and T. Miwa (1981) Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II. Phys. D 2 (3), pp. 407–448.
  • 5: Bibliography F
  • H. Flaschka and A. C. Newell (1980) Monodromy- and spectrum-preserving deformations. I. Comm. Math. Phys. 76 (1), pp. 65–116.
  • 6: Bibliography D
  • B. Dubrovin and M. Mazzocco (2000) Monodromy of certain Painlevé-VI transcendents and reflection groups. Invent. Math. 141 (1), pp. 55–147.
  • 7: Bibliography
  • V. I. Arnol’d, S. M. Guseĭn-Zade, and A. N. Varchenko (1988) Singularities of Differentiable Maps. Vol. II. Birkhäuser, Boston-Berlin.