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Topological classification of morse polynomials

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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 17 746 topological types of smooth functions with the same number of critical points, at most 426 types are realizable by polynomials of degree 4.

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References

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. I. Arnold

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  1. V. I. Arnold
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Vol. 268, pp. 40–55.

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Arnold, V.I. Topological classification of morse polynomials. Proc. Steklov Inst. Math. 268, 32–48 (2010). https://doi.org/10.1134/S0081543810010049

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  • DOI: https://doi.org/10.1134/S0081543810010049

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