Phase portraits of the gradient vector field

An eigenvalue and its associated eigenvector of the Hessian of p (a principal curvature and its associated axis) at a critical point define a onedimensional system. If the eigenvalue or curvature is negative, then p is a maximum at the critical point on this axis and a gradient vector will approach and terminate at this point from both its left- and right-hand side as illustrated in Fig. 2.6 for the case (1, — 1), a system of rank 1 and signature 

An analytical expression for a trajectory in the vicinity of a critical point is given in Section E2.2. While this expression is.necessary for numerical work, a knowledge of the phase portraits given above is all that is required for the definition of the elements of molecular structure which follows. 

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