Geodesic
On the real preimages of a real point under the Liashko–Looijenga covering for simple singularities
Izvestiya. Mathematics, Tome 43 (1994) no. 2, pp. 363-372 Cet article a éte moissonné depuis la source Math-Net.Ru

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The multiplicity of the Lyashko–Looijenga covering restricted to a connected component of the complement in $\mathbf R^\mu$ of the real bifurcation diagram of functions with a simple singularity, is expressed in terms of some discrete invariants of this component. For the case of the singularities $A_\mu$ an algorithm is indicated for finding these invariants from the full system of invariants of the component proposed by S. A. Barannikov. 
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M. R. Entov. On the real preimages of a real point under the Liashko–Looijenga covering for simple singularities. Izvestiya. Mathematics, Tome 43 (1994) no. 2, pp. 363-372. http://geodesic.mathdoc.fr/item/IM2_1994_43_2_a8/

[1] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii, t. 2, Nauka, M., 1984 | MR

[2] Arnold V. I., Vasilev V. A., Goryunov V. V., Lyashko O. V., “Osobennosti”, Itogi nauki i tekhn. Sovr. probl. matem. Fund. napravl., 6, VINITI, M., 1988, 1–256 | MR

[3] Livshits I. S., “Avtomorfizmy dopolneniya k bifurkatsionnomu mnozhestvu funktsii dlya prostykh osobennostei”, Funkts. analiz i ego prilozh., 15:1 (1981), 38–42 | MR | Zbl

[4] Looijenga E., “The complement of the bifurcation variety of a simple singularity”, Invent. Math., 23:2 (1974), 105–116 | DOI | MR | Zbl

[5] Lyashko O. V., “Geometriya bifurkatsionnykh diagramm”, Itogi nauki i tekhn. Sovrem. probl. matem., 22, VINITI, M., 1983, 94–129 | MR

[6] Lyashko O. V., “Raspadeniya prostykh osobennostei”, Funkts. analiz i ego prilozh., 10:2 (1976), 49–56 | Zbl

[7] Barannikov S. A., “O prostranstve veschestvennykh mnogochlenov bez kratnykh kriticheskikh znachenii”, Funkts. analiz i ego prilozh., 26:2 (1992), 10–17 | MR | Zbl

[8] Arnold V. J., “Bernoulli–Euler updown numbers, associated with functions singularities, their combinatories and arithmetics”, Duke Math. J., 63 (1991), 537–555 | DOI | MR | Zbl

[9] Arnold V. I., “Ischislenie zmei i kombinatorika chisel Bernulli, Eilera i Springera grupp Kokstera”, UMN, 47:1 (1992), 3–45 | MR