Geodesic
Topological classification of Morse polynomials
Informatics and Automation, Differential equations and topology. I, Tome 268 (2010), pp. 40-55

Voir la notice de l'article provenant de la source Math-Net.Ru

The topological classification is discussed for real polynomials of degree 4 in two real independent variables whose critical points and critical values are all different. It is proved that among the 17746 topological types of smooth functions with the same number of critical points, at most 426 types are realizable by polynomials of degree 4. 
@article{TRSPY_2010_268_a3,
     author = {V. I. Arnold},
     title = {Topological classification of {Morse} polynomials},
     journal = {Informatics and Automation},
     pages = {40--55},
     publisher = {mathdoc},
     volume = {268},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a3/}
}
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V. I. Arnold. Topological classification of Morse polynomials. Informatics and Automation, Differential equations and topology. I, Tome 268 (2010), pp. 40-55. http://geodesic.mathdoc.fr/item/TRSPY_2010_268_a3/