A note on chaos

AbstractLet f be a continuous function on a compact interval I. If some point in I has period 3 under f, then Li and Yorke have shown that f is chaotic. Nathanson has shown that if some point in I has period divisible by 3, 5, or 7 then f is chaotic. In this note it is shown that if some point has period p under, f, where p is not a power of 2, then f is chaotic. On the other hand for each p which is a power of 2 an example is given of a non-chaotic function with points of period p