monodromy groups

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1: 15.17 Mathematical Applications

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§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

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§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

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Monodromy of certain Painlevé-VI transcendents and reflection groups. Invent. Math. 141 (1), pp. 55–147.

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External Links:

ISSN 0020-9910, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.9(iii).

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4: Bibliography

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Singularities of Differentiable Maps. Vol. II. Birkhäuser, Boston-Berlin.

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Notes:

Monodromy and asymptotics of integrals, Translated from the Russian by Hugh Porteous, Translation revised by the authors and James Montaldi

External Links:

ISBN 0-8176-3185-2, MathReview, ZentralBlatt

Referenced by:

§36.12(iii).

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BibTeX

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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).

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Notes:

In Russian. English translation: Functional Anal. Appl., 6(1973), pp. 254–272.

External Links:

MathReview (G. R. Belickii), ZentralBlatt

Referenced by:

§36.2(i).

Encodings:

BibTeX

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Special Functions: Group Theoretical Aspects and Applications. D. Reidel Publishing Co., Dordrecht.

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Notes:

Reprinted by Kluwer Academic Publishers, Boston, 2001.

External Links:

ISBN 90-277-1822-9; 1-4020-0319-6, MathReview, ZentralBlatt

Referenced by:

Profile Richard A. Askey, Profile Tom H. Koornwinder.

Encodings:

BibTeX

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