From a point view of nonlinear dynamics, the electrical activity of the heart is a complex dynamical system, whose dynamics reflects the actual state of health of the heart. Nonlinear signal-processing methods are needed in order to accurately characterize these signals and improve understanding of cardiac arrhythmias. Recent developments on reconstructible signals and multiscale information content show that an analysis in terms of singularity exponents provides compact and meaningful descriptors of the structure and dynamics of the system. Such approach gives a compact representation atrial arrhythmic dynamics, which can sharply highlight regime transitions and arrhythmogenic areas.