fixed element | transformation fixed point

A point x^* which is mapped to itself under a map G, so that x^* = G(x^*). Such points are sometimes also called invariant points or fixed elements. Stable fixed points are called elliptical. Unstable fixed points, corresponding to an intersection of a stable and unstable invariant manifold, are called hyperbolic (or saddle). Points may also be called asymptotically stable (a.k.a. superstable).

critical point | involutory