Estimation of large-scale dimension densities - art. no. 016216

We propose a technique to calculate large-scale dimension densities in both higher-dimensional spatiotemporal systems and low-dimensional systems from only a few data points, where known methods usually have an unsatisfactory scaling behavior. This is mainly due to boundary and finite-size effects. With our rather simple method, we normalize boundary effects and get a sign ificant correction of the dimension estimate. This straightforward approach is based on rather general assumptions. So even weak coherent structures o btained from small spatial couplings can be detected with this method, Whic h is impossible by using the Lyapunov-dimension density. We demonstrate the efficiency of our technique for coupled logistic maps, coupled tent maps, the Lorenz attractor, and the Roessler attractor.