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Mosc. Math. J., 2015, Volume 15, Number 1, Pages 141–178 (Mi mmj554)  

This article is cited in 2 scientific papers (total in 2 papers)

The complete formal normal form for the Bogdanov–Takens singularity

Ewa Stróżynaa, Henryk Żołądekb

a Faculty of Mathematics and Information Sciences, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland
b Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland

Abstract: We solve completely the problem of formal classification of the vector fields of the form $\dot x=y+…$, $\dot y=…$ using formal changes of the coordinates but not of the time. In the proofs we avoid complicated calculations. The method we use is effective and can be applied in other classification problems.

Key words and phrases: nilpotent singularity, formal orbital normal form, non-orbital normal form.

DOI: https://doi.org/10.17323/1609-4514-2015-15-1-141-178

Full text: http://www.mathjournals.org/.../2015-015-001-009.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 05C38, 15A15; Secondary 05A15, 15A18
Received: August 8, 2012; in revised form July 19, 2014
Language:

Citation: Ewa Stróżyna, Henryk Żołądek, “The complete formal normal form for the Bogdanov–Takens singularity”, Mosc. Math. J., 15:1 (2015), 141–178

Citation in format AMSBIB
\Bibitem{StrĻ}
\by Ewa~Str\'o{\.z}yna, Henryk~{\.Z}o\l {\k a}dek
\paper The complete formal normal form for the Bogdanov--Takens singularity
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 1
\pages 141--178
\mathnet{http://mi.mathnet.ru/mmj554}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-1-141-178}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427417}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000354886200009}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Strozyna E., “Normal Forms For Germs of Vector Fields With Quadratic Leading Part. the Polynomial First Integral Case”, J. Differ. Equ., 259:11 (2015), 6718–6748  crossref  mathscinet  zmath  isi  elib  scopus
    2. E. Strozyna, “Normal forms for germs of vector fields with quadratic leading part. The remaining cases”, Studia Math., 239:2 (2017), 133–173  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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