Quasi-periodicity and dynamical systems: An experimentalist's view

J.A. Glazier, A. Libchaber
1988 IEEE Transactions on Circuits and Systems  
A great variety of natural and artificial systems exhibit chaos and frequency locking associated with quasi-periodicity. In this tutorial paper we present an overview of current theoretical and experimental work on quasi-periodicity. In Section I, we discuss the concept of universality and its relevance to experiments on nonlinear multifrequency systems. In Section 11, we describe the reduction of experimental data by means of Poincare sections, and the mathematical properties of the
more » ... onal circle map. In Section 111, we present the various dynamical systems techniques for determining scaling and multifractal properties as well as other more traditional methods of analysis. We emphaske the experimental observations that would support or refute the one-dimensional circle map model. In Section N, we summarize the experimental results, concentrating on forced Rayleigh-Benard convection and solid state systems. In Section V, we conclude with a brief discussion of the accomplishments and open problems of the dynamical systems theory of quasi-periodicity.
doi:10.1109/31.1826 fatcat:ctlizhxbmvgd3c4jz7c34atpqe