A more exact meaning of this condition will soon become clear. We shall only state that the condition signifies structural stability of a critical point. The point x = 0, on meeting conditions (2.31), (2.32), will be called a nondegenerate critical point. The above definitions are also applicable to the case of a function dependent on any number of variables (the matrix Vtj is the matrix of second derivatives of the function V). [Pg.52]

Palis and Smale s theorem of structural stability when used to describe structural changes in a molecular system predicts a configuration XeR to be structurally stable if p(r, X) has a finite number of critical points such that [Pg.21]

At the end of our considerations on nondegenerate critical points it should be emphasized that functions of the form (2.36) have a structurally stable critical point. Accordingly, in the systems described by Morse potential functions, catastrophes cannot occur. The structural stability of the function (2.36) will be demonstrated in the Appendix. [Pg.55]

© 2019 chempedia.info