The authors consider the well-known problem of solving for x in the equation x = F(x, &lgr;), where F(0,&lgr;)=0 and F is a smooth function of its arguments. The paper begins with a presentation of the standard theorem on the existence of bifurcation points and the stability of local bifurcation curves. It then appeals to a classical result by Krasnosl’skii that suggests an algorithm for constructing a bifurcation branch based on a nongenericity criterion, and computed from the adjoint operator obtained from the linearization of F. The methodology is then tested on the Lorenz system, which demonstrates the existence of a bifurcation point for this system’s double equilibrium point.

The paper is somewhat difficult to read. This is partly due to the inadequate use of language, but primarily because the proofs, which are relegated to an appendix, are only sketched. The references are mostly in Russian, so they may not be easily accessible.