Balanov, Zalman; Krasnov, Yakov On good deformations of \( A_m \)-singularities. (English) Zbl 1425.32026 Discrete Contin. Dyn. Syst., Ser. S 12, No. 7, 1851-1866 (2019). Summary: The standard way to study a compound singularity is to decompose it into the simpler ones using either blow up techniques or appropriate deformations. Among deformations, one distinguishes between miniversal deformations (related to deformations of a basis of the local algebra of singularity) and good deformations (one-parameter deformations with simple singularities coalescing into a multiple one). In concrete settings, explicit construction of a good deformation is an art rather than a science. In this paper, we discuss some cases important from the application viewpoint when explicit good deformations can be constructed and effectively used. Our applications include: (a) an \( n \)-dimensional Euler-Jacobi formula with simple and double roots, and (b) a simple approach to the known classification of phase portraits of planar differential systems around linearly non-zero equilibrium. Cited in 1 Document MSC: 32S30 Deformations of complex singularities; vanishing cycles 14B07 Deformations of singularities Keywords:good deformations; classification of multiple singularities; Euler-Jacobi formula; Grothendieck residue; planar differential systems PDFBibTeX XMLCite \textit{Z. Balanov} and \textit{Y. Krasnov}, Discrete Contin. Dyn. Syst., Ser. S 12, No. 7, 1851--1866 (2019; Zbl 1425.32026) Full Text: DOI