Editing Iterated function (section)

==Limiting behaviour==

Upon iteration, one may find that there are sets that shrink and converge towards a single point. In such a case, the point that is converged to is known as an [[attractive fixed point]]. Conversely, iteration may give the appearance of points diverging away from a single point; this would be the case for an [[unstable fixed point]].<ref>Istratescu, Vasile  (1981). ''Fixed Point Theory, An Introduction'',  D. Reidel, Holland.  {{ISBN|90-277-1224-7}}.</ref>

When the points of the orbit converge to one or more limits, the set of [[accumulation point]]s of the orbit is known as the '''[[limit set]]''' or the '''ω-limit set'''.

The ideas of attraction and repulsion generalize similarly; one may categorize iterates into [[stable manifold|stable set]]s and [[unstable set]]s, according to the behavior of small [[Neighbourhood (mathematics)|neighborhood]]s under iteration. Also see [[infinite compositions of analytic functions]].

Other limiting behaviors are possible; for example, [[wandering point]]s are points that move away, and never come back even close to where they started.