The cardiac electrical activity follows a complex dynamics whose accurate description is crucial to characterize arrythmias and classify their complexity. Rhythm reflects the connection topology of pacemaker cells at their source. Hence, characterizing the attractors as nonlinear, effective dynamics can capture the key parameters without imposing any particular model on the empirical signals. A dynamic phase-space reconstruction from appropriate embedding can be made robust and numerically stable with the presented method. Time series evolution is mapped to an object embedded in a phase space in abstract coordinates. With appropriate filtering, the method is robust and adapted to empirical signals. The result is a compact dynamical description that characterizes complexity degree and information distribution. Nonlinear analysis provides appropriate tools to characterize cardiac dynamics. Singularity analysis and phase-space reconstruction are physically meaningful complexity measures with minimal assumptions on the underlying models. We validate our approach on ECG, endocavitary catheter measures and electrocardiographic maps. Key parameters vary infrequently and exhibit sharp transitions, which show where information concentrates and correspond to actual dynamical regime changes. In space domain, extreme values highlight arrhythmogenic areas whose ablation stopped the fibrillation. We observe a correspondence of time lag fluctuations of phase-space reconstructions with atrial fibrillation episodes in the same way as with the dynamical changes coming from singularity exponents. This opens the way for improved model-independent complexity descriptors to be used in non-invasive, automatic diagnosis support and ablation guide for electrical insulation therapy, in cases of arrhythmias such as atrial flutter and fibrillation.