Saddle Point - Other Uses

Other Uses

In dynamical systems, a saddle point is a periodic point whose stable and unstable manifolds have a dimension that is not zero. If the dynamic is given by a differentiable map f then a point is hyperbolic if and only if the differential of ƒ n (where n is the period of the point) has no eigenvalue on the (complex) unit circle when computed at the point.

In a two-player zero sum game defined on a continuous space, the equilibrium point is a saddle point.

A saddle point is an element of the matrix which is both the largest element in its column and the smallest element in its row.

For a second-order linear autonomous systems, a critical point is a saddle point if the characteristic equation has one positive and one negative real eigenvalue.