Iterated function

In mathematics, an iterated function is a 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

• Iterated function @ Wikipedia

Function