On sufficient conditions for bifurcation

A new approach to bifurcation study is presented, relying on the theory of second order optimality conditions for abnormal constrained optimization problems developed earlier by the first author. This theory does not subsume the "primal" description of the feasible set (in terms of tangent vectors, or in any other way). As a result, the new sufficient conditions for bifurcation are obtained. These conditions are to some extent complementary with respect to the known bifurcation theory. Application to controllability problems is also discussed. Copyright (C) IFAC 2001.