A point 
which is mapped to itself under a map 
, so that 
. Such points are sometimes also called invariant
points or fixed elements (Woods 1961). 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).
Map Fixed Point
See also
Critical Point, InvolutoryExplore with Wolfram|Alpha
References
Shashkin, Yu. A. Fixed Points. Providence, RI: Amer. Math. Soc., 1991.Woods, F. S. Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry. New York: Dover, p. 14, 1961.Referenced on Wolfram|Alpha
Map Fixed PointCite this as:
Weisstein, Eric W. "Map Fixed Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MapFixedPoint.html