Give an example of a continuous function f, on an 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. let Define  by ....

Give an example of a continuous function f, on an 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.

let

Define
 by
. Show that f is transitive on I, but I has no periodic points of f.