Geodesic
Patchworking singularities~$A_\mu$ and~$D_\mu$ and meanders of their smoothing
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 193-217

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Let an algebraic curve $f$ have a singular point of type $A_{\mu}$ or $D_{\mu}$. Let $\tilde{f}$ be the curve obtained as a result of smoothing the singular point of the curve $f$. In this paper we study the local maximal meanders appearing under $M$-smoothing in a neighborhood of the singular point. A local maximal meander means that the number of real points of the intersection of the curve $\tilde{f}$ with a coordinate axis in the neighborhood is maximal and the points belong to one of the components of $\tilde{f}$; and an $M$-smoothing means that the number of components of the curve $\tilde{f}$, which appear in the neighborhood under the smoothing, is also maximal. 
@article{ZNSL_2003_299_a11,
     author = {A. B. Korchagin and D. E. Smith},
     title = {Patchworking singularities~$A_\mu$ and~$D_\mu$ and meanders of their smoothing},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {193--217},
     publisher = {mathdoc},
     volume = {299},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a11/}
}
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A. B. Korchagin; D. E. Smith. Patchworking singularities~$A_\mu$ and~$D_\mu$ and meanders of their smoothing. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 193-217. http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a11/