In bifurcation theory, a periodic orbit colliding with one of these points will produce a homoclinic bifurcation.
Korpelevich's (kor-PEH-leh-vich's) extraÂ·gradient method  nds sequences that converge to these entities. Along with the hyperbolic property of orbits, a dynamical system must not have any connections between these entities for the system to be topologically stable, according to the Andronov-Pontryagin (pon-tree-AH-gin) criterion. In bifurcation theory, a periodic orbit colliding with one of these points will produce a homoclinic bifurcation. An extension of Laplace's method continuously changes a contour integral to pass nearby these points to approximate integrals. The equation "z" equals "x cubed" minus "three x y-squared" de nes a "monkey" surface that is itself de ned by one of these points, which correspond to inde nite Hessian matrices. These non-extremal objects have a derivative equal to zero. For 10 points, name these points at which a multiÂ·variÂ·ate function simultaneously "curves up" and "curves down."
Korpelevich's (kor-PEH-leh-vich's) extraÂ·gradient method  nds sequences that converge to these entities.
saddle points [or minimax point; prompt on stationary point; prompt on critical points]