Branching equation of Andronov-Hopf bifurcation under group symmetry conditions

In branching theory of solutions of nonlinear equations group analysis methods [Ovsyannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978); Lectures on the Theory of Group Properties of Differential Equations (Novosibirsk University, Novosibirsk, 1966)] give the general approach for the construction of the complete form of branching equation and its subsequent investigation. These methods are applied here to the general situation of Andronov-Hopf bifurcation when there are some multiple semisimple eigenvalues on imaginary axis. (C) 1997 American Institute of Physics.