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Scaling Symmetries in Nonlinear Dynamics: A View from Parameter Space

Document Type

Article

Journal/Book Title/Conference

Physica D

Volume

81

Issue

1

Publication Date

2-15-1995

First Page

23

Last Page

31

Abstract

The orbit of the critical point of a discrete nonlinear dynamical system defines a family of polynomials in the parameter space of that system. We show here that for the important class of quadratic-like maps, these polynomials become indistinguishable under a suitable scaling transformation. The universal representation of these polynomials produced by such a scaling leads directly to accurate approximations for those parameter values where windows of order appear, the sizes of such windows, measures of window distortion, and the characterization of the internal structure of the windows in terms of generalized Feigenbaum numbers.

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Published by Elsevier in Physica D. Publisher PDF is available through link above. Publisher requires a subscription to access article.

https://doi.org/10.1016/0167-2789(94)00161-I

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