Difference between revisions of "Fixed point (mathematics)"
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Karl Jones (Talk | contribs) (Created page with "In mathematics, a '''fixed point''' (sometimes shortened to '''fixpoint''', also known as an '''invariant point''') of a function is an element...") |
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* [[Fixed-point theorems]] | * [[Fixed-point theorems]] | ||
* [[Fixed points of a Möbius transformation]] | * [[Fixed points of a Möbius transformation]] | ||
| − | * [[Function (mathematics) | + | * [[Function (mathematics)]] |
* [[Idempotent]] | * [[Idempotent]] | ||
* [[Infinite compositions of analytic functions]] | * [[Infinite compositions of analytic functions]] | ||
Revision as of 20:25, 23 September 2016
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's 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
- Fixed point (mathematics) @ Wikipedia
