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.

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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/

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