Determination of Fractal Dimension, Connection of Space and Temporal Chaos and Application to Experimental Results,

It has been observed in numerical studies of certain partial differential equations and of coupled maps that coherent spatial structures coexist with temporal chaos. From an experimental point of view spatial patterns have been quantitatively analysed in time-dependent chaotic regimes only in a few experiments. This report describes two of these experiments, where the chaotic states have been also quantitatively in terms of fractal dimension, metric entropy and lyapunov exponents. The method to compute these quantities are briefly summarized in the appendix. We first report experiments on surface waves instabilities, where the competition between two spatial patterns produces time dependent behavior and chaos. The results of this experiment are in good agreement with a low dimensional model obtained from Navier-Stokes equations. Next we describe experiments on time dependent behavior of a horizontal fluid layer, heated from below, that is Rayleigh-Benard convection. We show that time dependent regimes are characterized by the presence of either traveling waves or localized oscillations.