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Map 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 (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).


See also

Critical Point, Involutory

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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.

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Map Fixed Point

Cite this as:

Weisstein, Eric W. "Map Fixed Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MapFixedPoint.html

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