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

Current theoretical and experimental work on quasiperiodicity is reviewed in this tutorial. The concept of universality and its relevance to experiments on nonlinear multifrequency systems is discussed. The reduction of experimental data using Poincare sections and the mathematical properties of the one-dimensional circle map are considered. Various dynamical systems technique for determining scaling and multifractal properties as well as other more traditional methods of analysis, are presented. Experimental observations that would support or refute the one-dimensional circle map model are emphasized. Experimental results are summarized, with emphasis on forced Rayleigh-Benard convection and solid-state systems. Accomplishments and open problems of the dynamical systems theory of quasiperiodicity are outlined