ABSTRACT
In 1975, James Yorke teamed with T.-Y. Li to publish a paper entitled "Period Three Implies Chaos". This paper contains a proof of the Period 3 Theorem, a very special case of Sarkovskii's Theorem, which was at that time unknown in the West. The paper has become a landmark in that its title represents the first use of the word "Chaos" in the scientific literature. Yorke has made fundamental contributions in dynamical systems, particularly in the study of fractal basin boundaries and mathematical models for the spread of infectious diseases. Sarkovskii's Theorem, first proved in 1964, is an incredibly powerful and beautiful strengthening of the Period 3 Theorem. In 1964, A. N. Sarkovskii published a short paper that includes the theorem that now bears his name. Sarkovskii was one of the first mathematicians to suggest that iteration of functions of a real variable is a subject in its own right.
