Functional dimensionality of Koopman eigenfunction space

Ido Cohen; Eli Appleboim; Gershon Wolansky

doi:10.1016/j.rinam.2025.100585

Functional dimensionality of Koopman eigenfunction space

Ido Cohen
, Eli Appleboim
, Gershon Wolansky

Department of Electrical and Electronics Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

This work presents the general form solution of Koopman Partial Differential Equation for an autonomous system of N ordinary differential equations. We identify a domain in R^N for which any number in the complex plane is an eigenvalue of the Koopman operator, and all eigensolutions are obtained from N−1 functionally independent invariants of the system. Thus, we demonstrate that one may, in principle, diagonalize the system with only N functionally independent Koopman eigenfunctions.

Original language	English
Article number	100585
Journal	Results in Applied Mathematics
Volume	26
DOIs	https://doi.org/10.1016/j.rinam.2025.100585
State	Published - May 2025

Keywords

Conservation laws
Dynamical systems
Flowbox
Koopman operator
Koopman partial differential equation

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10.1016/j.rinam.2025.100585

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abstract = "This work presents the general form solution of Koopman Partial Differential Equation for an autonomous system of N ordinary differential equations. We identify a domain in RN for which any number in the complex plane is an eigenvalue of the Koopman operator, and all eigensolutions are obtained from N−1 functionally independent invariants of the system. Thus, we demonstrate that one may, in principle, diagonalize the system with only N functionally independent Koopman eigenfunctions.",

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N2 - This work presents the general form solution of Koopman Partial Differential Equation for an autonomous system of N ordinary differential equations. We identify a domain in RN for which any number in the complex plane is an eigenvalue of the Koopman operator, and all eigensolutions are obtained from N−1 functionally independent invariants of the system. Thus, we demonstrate that one may, in principle, diagonalize the system with only N functionally independent Koopman eigenfunctions.

AB - This work presents the general form solution of Koopman Partial Differential Equation for an autonomous system of N ordinary differential equations. We identify a domain in RN for which any number in the complex plane is an eigenvalue of the Koopman operator, and all eigensolutions are obtained from N−1 functionally independent invariants of the system. Thus, we demonstrate that one may, in principle, diagonalize the system with only N functionally independent Koopman eigenfunctions.

KW - Conservation laws

KW - Dynamical systems

KW - Flowbox

KW - Koopman operator

KW - Koopman partial differential equation

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Functional dimensionality of Koopman eigenfunction space

Abstract

Keywords

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