Geodesic
Variations on the Theme of Solvability by Radicals
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and singularities. Part 2, Tome 259 (2007), pp. 86-105.

Voir la notice de l'article provenant de la source Math-Net.Ru

We discuss the problem of representability and nonrepresentability of algebraic functions by radicals. We show that the Riemann surfaces of functions that are the inverses of Chebyshev polynomials are determined by their local behavior near branch points. We find lower bounds on the degrees of equations to which sufficiently general algebraic functions can be reduced by radicals. We also begin to classify rational functions of prime degree whose inverses are representable by radicals. 
@article{TM_2007_259_a6,
     author = {A. G. Khovanskii},
     title = {Variations on the {Theme} of {Solvability} by {Radicals}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {86--105},
     publisher = {mathdoc},
     volume = {259},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2007_259_a6/}
}
TY  - JOUR
AU  - A. G. Khovanskii
TI  - Variations on the Theme of Solvability by Radicals
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2007
SP  - 86
EP  - 105
VL  - 259
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2007_259_a6/
LA  - ru
ID  - TM_2007_259_a6
ER  - 
%0 Journal Article
%A A. G. Khovanskii
%T Variations on the Theme of Solvability by Radicals
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2007
%P 86-105
%V 259
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2007_259_a6/
%G ru
%F TM_2007_259_a6
A. G. Khovanskii. Variations on the Theme of Solvability by Radicals. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and singularities. Part 2, Tome 259 (2007), pp. 86-105. http://geodesic.mathdoc.fr/item/TM_2007_259_a6/

[1] Alekseev V. B., Teorema Abelya v zadachakh i resheniyakh, MTsNMO, M., 2001 | MR

[2] Arnold V. I., “Algebraicheskaya nerazreshimost problemy ustoichivosti po Lyapunovu i problemy topologicheskoi klassifikatsii osobykh tochek analiticheskoi sistemy differentsialnykh uravnenii”, Funkts. analiz i ego pril., 4:3 (1970), 1–9 | MR

[3] Arnold V. I., Oleinik O. A., “Topologiya deistvitelnykh algebraicheskikh mnogoobrazii”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 1979, no. 6, 7–17 | MR

[4] Arnold V. I., “Superpozitsii”, Kolmogorov A.N. Izbr. tr.: Matematika i mekhanika, Nauka, M., 1985, 444–451

[5] Arnold V. I., “Topologicheskoe dokazatelstvo transtsendentnosti abelevykh integralov v “Matematicheskikh nachalakh naturalnoi filosofii” Nyutona”, Ist.-mat. issled., 31 (1989), 7–17 | MR

[6] Arnol'd V. I., Vassil'ev V. A., “Newton's “Principia” read 300 years later”, Not. Amer. Math. Soc., 36:9 (1989), 1148–1154 ; “Addendum to: ‘Newton’s Principia read 300 years later' ”, 37:2 (1990), 144 | MR | MR

[7] Arnold V. I., “Problèmes résolubles et problèmes irrésolubles analytiques et géométriques”, Passion des formes. Dynamique qualitative, sémiophysique et intelligibilité, Dédié á René Thom, ENS Éditions, Fontenay–St.-Cloud, 1994, 411–417

[8] Arnold V. I., “Sur quelques problèmes de la théorie des systèmes dynamiques”, Topol. Meth. Nonlin. Anal., 4:2 (1994), 209–225 ; Арнольд В. И., “О некоторых задачах теории динамических систем”, Избранное–60, Фазис, М., 1997 | MR | Zbl | MR

[9] Arnold V. I., “I. G. Petrovskii, topologicheskie problemy Gilberta i sovremennaya matematika”, UMN, 57:4 (2002), 197–207 | MR

[10] Khovanskii A. G., “Topological obstructions to the representability of functions by quadratures”, J. Dyn. and Control Syst., 1:1 (1995), 91–123 | DOI | MR | Zbl

[11] Khovanskii A. G., “O razreshimosti i nerazreshimosti uravnenii v yavnom vide”, UMN, 59:4 (2004), 69–146 | MR | Zbl

[12] Berzhe M., Geometriya, T. 1, 2, Mir, M., 1984

[13] Khovanskii A. G., Teoriya Galua, nakrytiya i rimanovy poverkhnosti, MTsNMO, M., 2006

[14] Chebotarev N. G., Osnovy teorii Galua, Ch. 1, Editorial URSS, M., 2004

[15] Khovanskii A. G., Zdravkovska S., “Branched covers of $S^2$ and braid groups”, J. Knot Theory and Ramif., 5:1 (1996), 55–75 | DOI | MR