Frame, Michael; Peak, David Metric universality of order in one-dimensional dynamics. (English) Zbl 0870.58019 Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, No. 3, 567-572 (1993). Summary: The orbit of the critical point of a nonlinear dynamical system defines a family of functions in the parameter space of the system. For unimodal maps a renormalization makes these functions indistinguishable over a wide range of parameter values. The universal representation of these functions leads directly to a number of interesting results: (1) the positions in the parameter space of the windows of order; (2) the sizes of the windows of order; (3) measures of distortion in the window structure; and (4) various generalized Feigenbaum numbers. We explicitly discuss the examples of the quadratic and sine maps. MSC: 37E99 Low-dimensional dynamical systems Keywords:one-dimensional dynamics; quadratic map; sine maps PDFBibTeX XMLCite \textit{M. Frame} and \textit{D. Peak}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, No. 3, 567--572 (1993; Zbl 0870.58019) Full Text: DOI