View source for Iterated function

In [[mathematics]], an '''iterated function''' is a [[Function (mathematics)|function]] X → X (that is, a function from some set X to itself) which is obtained by composing another function f : X → X with itself a certain number of times.

== Description ==

The process of repeatedly applying the same function is called [[iteration]].

In this process, starting from some initial number, the result of applying a given function is fed again in the function as input, and this process is repeated.

Iterated functions are objects of study in computer science, fractals, dynamical systems, mathematics and renormalization group physics.

== See also ==

* [[Abel function]]
* [[Flow (mathematics)]]
* [[Fractional calculus]]
* [[Function (mathematics)]]
* [[Functional square root]]
* [[Infinite compositions of analytic functions]]
* [[Irrational rotation]]
* [[Iterated function system]]
* [[Iteration]]
* [[Iterative method]]
* [[Recurrence relation]]
* [[Rotation number]]
* [[Sarkovskii's theorem]]
* [[Schröder's equation]]

== External links ==

* [https://en.wikipedia.org/wiki/Iterated_function Iterated function] @ Wikipedia

[[Function]]
[[Category:Mathematics]]