On the numerical approximation of the Perron-Frobenius and Koopman operator

Understand

Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system.

• Examples of such operators are the Perron-Frobenius and the Koopman operator.
• In this paper, we will review different methods that have been developed over the last decades to compute finite-dimensional approximations of these infinite-dimensional operators - e.g.
• Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and differences between these approaches.