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Mosc. Math. J., 2011, Volume 11, Number 2, Pages 259–263 (Mi mmj420)  

This article is cited in 1 scientific paper (total in 1 paper)

Weak total rigidity for polynomial vector fields of arbitrary degree

Yu. Ilyashenkoabcd

a Moscow State University
b Steklov Math. Institute, Moscow, RUSSIA
c Moscow Independent University
d Cornell University, US

Abstract: We prove that in the space of the polynomial vector fields of arbitrary degree $n$ with $n+1$ different singular points at infinity the set of vector fields that are orbitally topologically equivelent to a generic vector field (modulo affine equivalence) is no more than countable.
This is the second one of two closely related papers. It was started after the first one, “Total rigidity of generic quadratic vector fields”, was completed. The present paper is motivated by the problem stated at the end of the first paper. The problem remains open. A slightly weaker problem is solved below.
This paper is independent on the first one. For the sake of convinience, it is published first.

Key words and phrases: foliations, topological equivalence, rigidity.

DOI: https://doi.org/10.17323/1609-4514-2011-11-2-259-263

Full text: http://www.ams.org/.../abst11-2-2011.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 37F75
Received: October 10, 2010
Language:

Citation: Yu. Ilyashenko, “Weak total rigidity for polynomial vector fields of arbitrary degree”, Mosc. Math. J., 11:2 (2011), 259–263

Citation in format AMSBIB
\Bibitem{Ily11}
\by Yu.~Ilyashenko
\paper Weak total rigidity for polynomial vector fields of arbitrary degree
\jour Mosc. Math.~J.
\yr 2011
\vol 11
\issue 2
\pages 259--263
\mathnet{http://mi.mathnet.ru/mmj420}
\crossref{https://doi.org/10.17323/1609-4514-2011-11-2-259-263}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2859236}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000288967100004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. Ilyashenko, V. Moldavskis, “Total rigidity of generic quadratic vector fields”, Mosc. Math. J., 11:3 (2011), 521–530  mathnet  crossref  mathscinet
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