Brucks, K.; Galeeva, R.; Mumbrú, P.; Rockmore, D.; Tresser, C. On the *-product in kneading theory. (English) Zbl 0880.54025 Fundam. Math. 152, No. 3, 189-209 (1997). 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. Reviewer: T.Nowicki (Warszawa) Cited in 5 Documents MSC: 54H20 Topological dynamics (MSC2010) 37E99 Low-dimensional dynamical systems Keywords:renormalization; kneading; *-product; multimodal maps; linear interpolation Citations:Zbl 0664.58015 PDFBibTeX XMLCite \textit{K. Brucks} et al., Fundam. Math. 152, No. 3, 189--209 (1997; Zbl 0880.54025) Full Text: EuDML