Iteration of Differentiable Functions under m-Modal Maps with Aperiodic Kneading Sequences

We consider the dynamical system A, T , where A is a class of differentiable functions defined on some interval and T:A→A is the operator Tφ:foφ, where f is a differentiable m-modal map. Using an algorithm, we obtained some numerical and symbolic results related to the frequencies of occurrence of critical values of the iterated functions when the kneading sequences of f are aperiodic. Moreover, we analyze the evolution as well as the distribution of the aperiodic critical values of the iterated functions