An Analysis of Bifurcation Points of Nonlinear Equations Satisfying a Condition
Norio Yamamoto · Institutional Repositories DataBase (IRDB) · 1985
We consider bifurcation points of a parameter-dependent nonlinear equation F(x, B)=0 whose left member F(x, B) satisfies the condition F(Sx, B)=SF(x, B) for a matrix S which has eigenvalues ±1. If the x-component x^^^ of a bifurcation point (x^^^, B^^^) is an eigenvector corresponding to the eigenvalue 1 (or-1) of the matrix S, then we can compute (x^^^, B^^^) with high accuracy in a way using an augmented system of nonlinear equations which contains the equation F(x, B)=0. Moreover we also give a necessary and sufficient condition for guaranteeing the isolatedness of such a bifurcation point.