Fixed point (mathematics)

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