Loading [MathJax]/jax/output/CommonHTML/config.js
Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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
\Bibitem{Arn10}
\by V.~I.~Arnold
\paper Topological classification of Morse polynomials
\inbook Differential equations and topology.~I
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2010
\vol 268
\pages 40--55
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm2866}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2724333}
\zmath{https://zbmath.org/?q=an:1214.57026}
\elib{https://elibrary.ru/item.asp?id=13726632}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2010
\vol 268
\pages 32--48
\crossref{https://doi.org/10.1134/S0081543810010049}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000277345600004}
\elib{https://elibrary.ru/item.asp?id=15332216}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952250451}
Linking options:
  • https://www.mathnet.ru/eng/tm2866
  • https://www.mathnet.ru/eng/tm/v268/p40
    • This publication is cited in the following 3 articles:
    1. M. V. Meshcheryakov, “Classification of taut irreducible real linear representations of compact connected Lie groups”, St. Petersburg Math. J., 32:1 (2021), 31–38  mathnet  crossref  isi  elib
    2. Maksymenko S., “Deformations of Functions on Surfaces By Isotopic to the Identity Diffeomorphisms”, Topology Appl., 282 (2020), 107312  crossref  mathscinet  isi
    3. E. A. Kudryavtseva, “On the homotopy type of spaces of Morse functions on surfaces”, Sb. Math., 204:1 (2013), 75–113  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Statistics & downloads:
    Abstract page:1084
    Full-text PDF :247
    References:237
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025