The Question: Give an example of a continuous function, $f$, on the interval, $I$, such that the set of periodic points of $f$ is dense in $I$, but f does not have sensitive dependence on initial conditions.
The Attempt: I tried using a trig function, so suppose $f(x)=cos(x)$. I am not entirely sure if I am supposed to define a set for I. However, I need to show that $cos(x)$ is dense in I but it is not sensitive dependent on initial conditions. Can you give me some pointers or comments on how I can prove this?