View source for Fixed point (mathematics)

In [[mathematics]], a '''fixed point''' (sometimes shortened to '''fixpoint''', also known as an '''invariant point''') of a [[Function (mathematics)|function]] is an element of the function's [[Domain of a function|domain]] that is mapped to itself by the function.

== Description ==

Points that come back to the same value after a finite number of iterations of the function are called periodic points. A fixed point is a periodic point with period equal to one. In projective geometry, a fixed point of a projectivity has been called a double point.

In [[Galois theory]], the set of the fixed points of a set of field automorphisms is a field called the fixed field of the set of automorphisms.

== See also ==

* [[Eigenvector]]
* [[Equilibrium]]
* [[Fixed-point combinator]]
* [[Fixed-point subgroup]]
* [[Fixed-point subring]]
* [[Fixed-point theorems]]
* [[Fixed points of a Möbius transformation]]
* [[Function (mathematics)]]
* [[Idempotent]]
* [[Infinite compositions of analytic functions]]
* [[Invariant (mathematics)]]

== External links ==

* [https://en.wikipedia.org/wiki/Fixed_point_(mathematics) Fixed point (mathematics)] @ Wikipedia

[[Category:Functions]]
[[Category:Mathematics]]