Geodesic
Minimal morsifications for functions of two real variables
Čebyševskij sbornik, Tome 21 (2020) no. 1, pp. 381-387 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we give an explicit construction of morsifications with the smallest topologically possible number of real critical points for functions of two variables with smooth level-set branches, as well as for semiquasihomogenous functions of two real variables.
Keywords: curve singularities, deformations of singularities, real curves
Mots-clés : semiquasihomogenous functions. 
@article{CHEB_2020_21_1_a26,
     author = {I. A. Proskurnin},
     title = {Minimal morsifications for functions of two real variables},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {381--387},
     year = {2020},
     volume = {21},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_1_a26/}
}
TY  - JOUR
AU  - I. A. Proskurnin
TI  - Minimal morsifications for functions of two real variables
JO  - Čebyševskij sbornik
PY  - 2020
SP  - 381
EP  - 387
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CHEB_2020_21_1_a26/
LA  - ru
ID  - CHEB_2020_21_1_a26
ER  - 
%0 Journal Article
%A I. A. Proskurnin
%T Minimal morsifications for functions of two real variables
%J Čebyševskij sbornik
%D 2020
%P 381-387
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/CHEB_2020_21_1_a26/
%G ru
%F CHEB_2020_21_1_a26
I. A. Proskurnin. Minimal morsifications for functions of two real variables. Čebyševskij sbornik, Tome 21 (2020) no. 1, pp. 381-387. http://geodesic.mathdoc.fr/item/CHEB_2020_21_1_a26/

[1] V. I. Arnol'd, “Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures”, Funct. Anal. Appl., 12:1 (1978), 1–12 | Zbl

[2] Gusein-Zade S. M., “On a problem of B. Teissier”, Topics in Singularity Theory, V. I. Arnold's 60th Anniversary Collection, eds. A. Khovanskii, A. Varchenko, V. Vassiliev, Am. Math. Soc., Providence, Rhode Island, 1997, 117–141 | MR

[3] Gusein-Zade S. M., “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 | MR | Zbl

[4] Gonzalez-Ramirez J. A., Luengo I., “Deformations of functions without real critical points”, Communications in Algebra, 31:9 (2003), 42–55 | DOI | MR

[5] Casas-Alvero E., Singularities of plane curves, Cambridge university press, New York, 2000 | MR | Zbl

[6] Milnor J., Singular Points of Complex Hypersurfaces, Princeton university press, Princeton, New Jersey, 1968 | MR | Zbl

[7] Damon J., “On the number of branches for real and complex weighted homogeneous curve singularities”, Topology, 30:2 (1991), 223–229 | DOI | MR | Zbl