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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.

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
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