Correia, Maria de Fátima; Ramos, Carlos; Vinagre, Sandra Symbolic dynamics for iterated smooth functions. (English) Zbl 1221.37023 Grazer Math. Ber. 354, 26-36 (2009). Summary: We consider the discrete dynamical system \(({\mathcal A},T)\), where \({\mathcal A}\) is a class of smooth real functions defined on some interval and \(T:{\mathcal A}\to{\mathcal A}\) is an operator \(T\varphi:=f\circ\varphi\), where \(f\) is a function on the real line. Iteration of smooth maps appears naturally in the study of continuous difference equations and boundary value problems. In our work we develop some techniques of symbolic dynamics for the discrete dynamical system \(({\mathcal A},T)\). We analyze in detail the case in which \(T\) arises form unimodal interval maps. Cited in 3 Documents MSC: 37B10 Symbolic dynamics 39B12 Iteration theory, iterative and composite equations 37C05 Dynamical systems involving smooth mappings and diffeomorphisms 26A18 Iteration of real functions in one variable Keywords:symbolic dynamics; infinite-dimensional dynamical systems; iteration theory; smooth maps; one-dimensional maps PDFBibTeX XMLCite \textit{M. de F. Correia} et al., Grazer Math. Ber. 354, 26--36 (2009; Zbl 1221.37023)