On the versality of a family of symmetric vector fields in the plane

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.
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Bibliography: 11 titles.