Geodesic
On the versality of a~family of symmetric vector fields in the plane
Sbornik. Mathematics, Tome 48 (1984) no. 2, pp. 463-492

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The case is considered of a critical fixed point of a diffeomorphism of codimension 2 whose linear part has the eigenvalues $\pm1$. 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. 
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Kh. Zholondek. On the versality of a~family of symmetric vector fields in the plane. Sbornik. Mathematics, Tome 48 (1984) no. 2, pp. 463-492. http://geodesic.mathdoc.fr/item/SM_1984_48_2_a11/