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.