Evidencing chaos from dimensions?

Many algorithms, aimed at discriminating deterministic chaos from stochastic noise, are based on the estimation of some (fractal) dimensions in a reconstructed phase-space. We emphasize the fact that misleading results can be obtained when the signals under study exhibit themselves some fractal properties. Current methods are therefore revisited in order to provide “dimension” informations which are more directly related to the number of degrees of freedom involved in the dynamics of a system rather than to the purely geometrical structure of its reconstructed attractor. This is essentially achieved by extending existing second-order techniques up to fourth-order