Took Dr. Yorke’s undergraduate course on dynamical systems at Maryland. By far my favorite course ever. Interesting to note that the result discussed in this paper was independently discovered a few years earlier by Sharkovskii [1].
How cool that would have been. Would love to hear about any of the class gems, insight or otherwise. What year did you attend?
From the wiki page, I am led to believe that he proved a weaker result, being that if there are cycles of period three then there are cycles of every period (which is not the period three implies chaos result).
See the second paragraph in the section 'Generalizations'.