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

Abstract EN

We consider the dynamical system (?, T), where ? is a class of differentiable functions defined on some interval and T : ? → ? is the operator Tϕ:=f∘ϕ, 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.