Given a function

and an initial value

, the sequence of iterates of

is the sequence defined recursively by

. If

, then

. If

is smaller than one in absolute value, then clearly

, which is the solution to the equation

. If

>1, then the sequence of iterates diverges to infinity or minus infinity depending on the sign of

; that is, depending on which side of the fixed point the sequence of iterates starts. If

, then the sequence of iterates alternates between values to the left and right of the fixed point whose distance from the fixed point grows without bound.