Minimal deformations of semihomogenous vector fields
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1473-1482 Cet article a éte moissonné depuis la source Math-Net.Ru

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For any semihomogenous vector field on a real plane we construct a deformation with a minimal topologically possible number of singular points.
Keywords: singularities, deformations of singularities, plane vector fields, curve singularities.
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I. A. Proskurnin. Minimal deformations of semihomogenous vector fields. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1473-1482. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a24/

[1] J. Palis, C.C. Pugh, “Fifty problems in dynamical systems”, Dynamical Systems (Warwick, 1974), Lect. Notes Math., 468, eds. Manning, A., Springer, Berlin–Heidelberg, 1975, 345–353 | DOI | Zbl

[2] C.P. Simon, C.J. Titus, “Removing index-zero singularities with $C^1$-small perturbations”, Dynamical Systems (Warwick, 1974), Lect. Notes Math., 468, eds. Manning, A., Springer, Berlin, Heidelberg, 1975, 278–286 | DOI | Zbl

[3] D. Anker, “On removing isolated zeroes of vector felds by perturbation”, Nonlinear Anal., Theory Methods Appl., 8 (1984), 1095–1112 | DOI | Zbl

[4] A. Coffman, J. Lebl, “Removing isolated zeroes by homotopy”, Topol. Methods Nonlinear Anal., 54:1 (2019), 275–296 | Zbl

[5] S.M. Gusein-Zade, “On the existence of deformations without critical points (the Teissier problem for functions of two variables)”, Funct. Anal. Appl., 31:1 (1997), 58–60 | DOI | Zbl

[6] V.A. Vassiliev, “A few problems on monodromy and discriminants”, Arnold Math J., 1:2 (2015), 201–209 | DOI | Zbl

[7] V.I. Arnol'd, S.M. Gusein-Zade, A.N. Varchenko, Singularities of diferentiable maps, Birkhauser, Boston-Basel-Berlin, 1985 | Zbl

[8] J. Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, 61, Princeton University Press, Princeton, 1968 | Zbl

[9] E. Bierstone, P.D. Milman, “Semianalytic and subanalytic sets”, Publ. Math., Inst. Hautes Étud. Sci., 67 (1988), 5–42 | DOI | Zbl

[10] M.A. Krasnosel'skii, A.I. Perov, A.I. Povolotskiy, P.P. Zabrejko, Plane vector fields, Academic Press, New York–London, 1966 | Zbl