×

Kneading sequences and characteristic sets of Feigenbaum’s maps. (Chinese. English summary) Zbl 1119.37011

Summary: Let \(f\) be a Feigenbaum map, i.e., a unimodal solution satisfying certain conditions of the functional equation \(f^p(\lambda x)=\lambda f(x)\). The kneading sequence of \(f\) is a 0–1 infinite sequence and the characteristic set of \(f\) is the closure of the orbit of the critical point. We investigate properties of \(f\) and we prove that the kneading sequence of \(f\) is a fixed point of some substitution in a symbolic space and the restriction of \(f\) to the characteristic set is a factor of some substitution subshift.

MSC:

37B10 Symbolic dynamics
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37E20 Universality and renormalization of dynamical systems
PDFBibTeX XMLCite