Abstract:
The case is considered of a critical fixed point of a diffeomorphism of codimension 2 whose linear part has the eigenvalues ±1. According to ideas developed by Takens and Arnol'd, to deformations of such diffeomorphisms there correspond families of vector fields invariant with respect to an involution of the plane, namely, a reflection relative to a line passing through the fixed point. Bifurcations in two-parameter families in general position are described. Rigorous proofs are given.
Figures: 2.
Bibliography: 11 titles.
\Bibitem{Zho83}
\by Kh.~Zholondek
\paper On the versality of a~family of symmetric vector fields in the plane
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 2
\pages 463--492
\mathnet{http://mi.mathnet.ru/eng/sm2142}
\crossref{https://doi.org/10.1070/SM1984v048n02ABEH002686}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=695955}
\zmath{https://zbmath.org/?q=an:0554.58041|0516.58032}
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