Direct determination of the f(α) singularity spectrum

Abstract

The direct determination of the f(\ensuremath{\alpha}) singularity spectrum from experimental data is a difficult problem. This Letter introduces a simple method for computing f(\ensuremath{\alpha}) based on the theorems of Shannon, Eggelston, and Billingsley which is markedly superior to other recently proposed methods, especially when dealing with experimental data from low-dimensional chaotic systems where the underlying dynamics are unknown.