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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 268, Pages 40–55 (Mi tm2866)  
This article is cited in 3 scientific papers (total in 3 papers)

Topological classification of Morse polynomials

V. I. Arnold

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (205 kB) Citations (3)
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Abstract: 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.
Received in July 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 268, Pages 32–48
DOI: https://doi.org/10.1134/S0081543810010049
Bibliographic databases:
Document Type: Article
UDC: 517.988
Language: Russian
Citation: V. I. Arnold, “Topological classification of Morse polynomials”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 40–55; Proc. Steklov Inst. Math., 268 (2010), 32–48
Citation in format AMSBIB
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\paper Topological classification of Morse polynomials
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\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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