SIMPLE LABORATORY INSTRUMENTATION FOR MEASURING POINTWISE DIMENSIONS FROM CHAOTIC TIME-SERIES

An analog instrumentation for estimating dimensions of chaotic dynamic al systems has been developed. The technique employs time series of th e Poincare points successively displayed on the screen of an oscillosc ope. It provides a rapid way to estimate the pointwise dimension from a single variable directly in an experiment. The instrumentation is ea sy to build and is convenient to employ. We have tested it by applying to periodic and quasiperiodic oscillators, and have verified by means of the fractal two-dimensional Poincare map, simulated from the Duffi ng-Holmes differential equation. The measured values well agree with t he computer calculated ones.