A linear operator acting on function spaces that describes how density distributions evolve under a deterministic dynamical system, effectively tracking the evolution of probability measures.
- Essential for modeling chaos, predicting long-term behavior, studying Molecular Dynamics, and identifying metastable sets.
Relation to Koopman Operator: While the Perron–Frobenius operator tracks the evolution of densities (push-forward), the Koopman operator tracks the evolution of observables (pull-back).