BIFURCATIONAL INDETERMINACY AND FLUCTUATION OF BRANCH-POINTS UNDER CONDITIONS OF SINGULAR PERTURBATION

The concept of bifurcational instability is introduced, with particular reference to solutions of the Marguerre-Vlasov problem, in which the coefficient of the highest-order derivative is a natural small parameter mu. An instability criterion is formulated, together with an algorithm for its computation in the case when mu << 1. A method is presented for the numerical and bifurcational analysis of the fluctuation of branch points. It is shown that perturbation of the coefficients in the problem may bring about a change in the type of bifurcation, the rotation group of the eigenfunctions and the multiplicity v of, for example, the first eigenvalue. An upper bound of the type O (mu-1/2),mu << 1 is presented.