A 1975 paper by Tien-Yien Li and James A. Yorke, proving the suprising result that in any

one-dimensional system, if there is a

periodic orbit with period three (equivalently, a point with such an orbit), then there must be periodic orbits of any period, as well as

chaotic (

aperiodic) orbits.

This paper led to the realization that chaos was actually a common phenomenon in physical systems, as well as popularizing the term "chaos".

A special case of our main result says that if there is a periodic point with period 3, then for each integer *n* = 1, 2, 3, ..., there is a periodic point with period *n*. Furthermore, there is an uncountable subset of points *x* in *J* which are not even "asymptotically periodic."
--Li & Yorke, "Period Three Implies Chaos"

*American Mathematical Monthly*, Vol. 82 No. 10, 985-992.