Transient periodicity in chaos

Chaotic time series can exhibit rare bursts of “periodic” motion. We discuss one mechanism for this phenomenon of “transient periodicity”: the trajectory gets temporarily stuck in the neighborhood of a semiperiodic “semi-attractor” (or “chaotic saddle”). This can provide insight for interpreting such phenomena in empirical time series; it also allows for a novel partition of the phase space, in which the attractor may be viewed as the union of many such chaotic saddles