Mathematics Senior Capstone Papers

Document Type


Publication Date

Spring 5-12-2020


The number of periodic points of a function depends on the context. The number of complex periodic points and rational periodic points have been shown to be infinite and finite, respectively, if f is a polynomial of degree at least 2. However, the number of real periodic points can be either finite or infinite. Sharkovskys Theorem states that if p is left of q in the “Sharkovsky ordering” and the continuous function f has a point of period p, then f also has a point of period q. This statement becomes very powerful when considering a function that has points of period 3, all the way to the left side of the Sharkovsky ordering, since having a point of period 3 implies the existence of points of all periods. We explore a continuous function with points of period 3 where the function can be restricted to an interval containing points of period all other natural numbers.