BIFURCATION, POTENTIALITY, GROUP-THEORETICAL AND ITERATIVE METHODS

General theorems for potentiality of branching equation (BEq) are esta blished. With the aid of M.Morse theory in its strengthening Conley's variant applied to potential BEq the general theorems about bifurcatio n points and surfaces are established. Thus We extend the ideas of max imal using of finite-dimensionality of BEq. Note here that the idea of degree theory application to BEq directly as realized for the first t ime in our work in 1971 [15]. Our approach allows to eliminate the res trictive requirement of potentiality of original nonlinear equation. U sing group theoretic methods we construct the general form of the BEq symmetric with respect to fundamental representations of the rotations groups and on the basis of this form propose iterative methods for ca lculating solutions depending on free parameters in a neighborhood of a bifurcation point. Here the general theorems [1] about potentiality of branching equation (BEq) are proved and as corollaries from them ou r recent results [2-4] are obtained. With the aid of M.Morse theory in its strengthening Conley's variant [5] the general theorems about bif urcation points and surfaces and as corollaries the results [6-8] are obtained. These results for rotation group symmetry conditions allow t o give iterative methods for the determination of small branching solu tions depending on free parameters in a neighborhood of a bifurcation point [9].