An operator method for approximate investigation of a regular bifurcation in multiparameter dynamical systems

A new operator method for investigating a large class of bifurcation problems with multidimensional degenerations is considered. The method makes it possible to detect bifurcation parameter values; it leads to an iteration procedure and asymptotic formulae for approximate investigation of problems depending on many parameters. Applications to the theory of dynamical systems are discussed, e.g. in problems on bifurcation of fixed points, forced oscillations and self-oscillations.