Iteration of Differentiable Functions underm-Modal Maps with Aperiodic Kneading Sequences

Abstract

We consider the dynamical system (, ), where is a class of differentiable functions defined on some interval and : → is the operator , where 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 are aperiodic. Moreover, we analyze the evolution as well as the distribution of the aperiodic critical values of the iterated functions.