SUBSTITUTION SYSTEMS ASSOCIATED WITH THE DYNAMICAL SYSTEM (A,Tf)

Abstract

We consider the dynamical system (A,Tf), where A is a class of differentiable real functions defined on some interval and Tf:A→A is an operator Tf:=foφ, where f is a differentiable m-modal map. If we consider functions in A whose critical values are periodic points for f then, we show how to define and characterize a substitution system associated with (A,Tf). For these substitution systems, we compute the growth rate of the new critical points, and observe that this growth is independent of the initial conditions.