The decomposition of the state space of a dynamical system into almost invariant sets is important for understanding its essential macroscopic behavior. The concept is reasonably well understood for autonomous dynamical systems, and recently a generalization appeared for non-autonomous systems: coherent sets. Methods for identifying coherent sets, and Lagrangian coherent structures more generally, rely on coherence being present throughout a specified time interval. In reality, coherent structures are ephemeral, continually appearing and disappearing. We present a new construction, based on the dynamic Laplacian, that relaxes this materiality requirement in a natural way, and provides the means to resolve the births, lifetimes, and deaths of coherent structures.
invited by Sebastian Reich