Solutions stability on linear approximation to Cauchy problem , branching equation in the root subspace, symmetry

V. A. Trenogin results [7, 8] about solutions stability to Cauchy problem for differential equations in Banach space on linear approximation in the case of degenerate linearization are presented from the point of view of bifurcation equation in the root subspace. Conclusions are made for the presence of group and non-group symmetries.