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Moscow Mathematical Journal, 2015, Volume 15, Number 1, Pages 141–178
DOI: https://doi.org/10.17323/1609-4514-2015-15-1-141-178 (Mi mmj554) 		 
This article is cited in 13 scientific papers (total in 13 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
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DOI: https://doi.org/10.17323/1609-4514-2015-15-1-141-178
Abstract: We solve completely the problem of formal classification of the vector fields of the form $\dot x=y+\dots$, $\dot y=\dots$ 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.
Received: August 8, 2012; in revised form July 19, 2014
Bibliographic databases:
Document Type: Article
MSC: Primary 05C38, 15A15; Secondary 05A15, 15A18
Language: English
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
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\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://mathscinet.ams.org/mathscinet-getitem?mr=3427417}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000354886200009}
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    • This publication is cited in the following 13 articles:
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