All Physics Faculty Publications

Title

Metric Universality of Order in One-Dimensional Dynamics

Document Type

Article

Journal/Book Title/Conference

International Journal of Bifurcation and Chaos

Volume

6

Issue

3

Publication Date

1993

First Page

567

Last Page

572

DOI

10.1142/S0218127493000453

Abstract

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.

Comments

Originally published by World Scientific in the International Journal of Bifurcation and Chaos. Subscription is required to access article.

http://www.worldscinet.com/ijbc/03/0303/S0218127493000453.html