Abstract: The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition; this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics.

The Koopman operator is also known as the composition operator, which is formally the pull-back operator on the space of scalar observable functions . The Koopman operator is the dual, or left-adjoint, of the Perron-Frobenius operator, or transfer operator, which is the push-forward operator on the space of probability density functions. Oct 22, 2015 · Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for control by Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, and J. Nathan Kutz For more ...

Abstract In a prior paper, the author generalized the classical factor theorem of Sinai to actions of arbitrary countably infinite groups. In the present paper, we use this theorem and the techniques of its proof in order to study connections between positive entropy phenomena and the Koopman representation.

of the Koopman eigenfunctions. Overall, the “tuples” of Koopman eigenfunctions, eigenvalues, and modes enable us to: (a) transform state space so that the dynamics appear to be linear, (b) determine the temporal dynamics of the linear system, and (c) reconstruct the state of the original system from our new linear representation. In