Kurakin, L. G.; Yudovich, V. I. On equilibrium bifurcations in the cosymmetry collapse of a dynamical system. (Russian, English) Zbl 1049.37040 Sib. Mat. Zh. 45, No. 2, 356-374 (2004); translation in Sib. Math. J. 45, No. 2, 294-310 (2004). The authors study the bifurcations that accompany the collapse of a continuous family of equilibria of a cosymmetric dynamical system (or a family of solutions to a cosymmetric operator equation in general) under some perturbation that destroys cosymmetry. Using the Lyapunov-Schmidt method, they study in detail the cases in which the branching equation is one- or two-dimensional. Reviewer: S. A. Treskov (Novosibirsk) Cited in 1 Document MSC: 37G40 Dynamical aspects of symmetries, equivariant bifurcation theory 37L10 Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems 47J15 Abstract bifurcation theory involving nonlinear operators Keywords:cosymmetry; symmetry; bifurcation; family of equilibria; Lyapunov-Schmidt method PDFBibTeX XMLCite \textit{L. G. Kurakin} and \textit{V. I. Yudovich}, Sib. Mat. Zh. 45, No. 2, 356--374 (2004; Zbl 1049.37040); translation in Sib. Math. J. 45, No. 2, 294--310 (2004) Full Text: EuDML