×

On the *-product in kneading theory. (English) Zbl 0880.54025

The kneading theory describes the rules of coding the dynamics of a piecewise monotone interval self map into sequences of symbols representing the monotone branches and turning points. The unimodal case (three symbols) is well understood [J. Milnor and W. Thurston, Lect. Notes Math. 1342, 465-563 (1988; Zbl 0664.58015)] and a range of properties of the map may be read from the kneading sequence of the turning point, which is a topological invariant. The *-product of a finite and an infinite sequence is a substitution rule, corresponding maps are renormalizable. The paper discusses a generalization (and its limits) of this notion to multimodal maps and analyzes some special cases using the piecewise linear maps which interpolate the permutation of a finite set.

MSC:

54H20 Topological dynamics (MSC2010)
37E99 Low-dimensional dynamical systems

Citations:

Zbl 0664.58015
PDFBibTeX XMLCite
Full Text: EuDML