Iteration theory has its roots in the operation of substituting functions into itself. This has led to questions like that of the behaviour of functions by repeating this substitution and when the number of iterations tends to infinity. The terms ''orbit'' and ''chaos'' appropriately describe this behaviour. Dynamical systems and the theory of functional equations play important roles in this field.

Iteration theory has its roots in the operation of substituting functions into itself. This has led to questions like that of the behaviour of functions by repeating this substitution and when the number of iterations tends to infinity. The terms ''orbit'' and ''chaos'' appropriately describe this behaviour. Dynamical systems and the theory of functional equations play important roles in this field.