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

Access to Document

10.1016/j.rinam.2025.100585

Cite this

@article{46ab13a003f845d3aa09f6ef36a84f66,

title = "Functional dimensionality of Koopman eigenfunction space",

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.",

keywords = "Conservation laws, Dynamical systems, Flowbox, Koopman operator, Koopman partial differential equation",

author = "Ido Cohen and Eli Appleboim and Gershon Wolansky",

note = "Publisher Copyright: {\textcopyright} 2025",

year = "2025",

month = may,

doi = "10.1016/j.rinam.2025.100585",

language = "אנגלית",

volume = "26",

journal = "Results in Applied Mathematics",

issn = "2590-0374",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Functional dimensionality of Koopman eigenfunction space

AU - Cohen, Ido

AU - Appleboim, Eli

AU - Wolansky, Gershon

PY - 2025/5

Y1 - 2025/5

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

UR - http://www.scopus.com/inward/record.url?scp=105006876714&partnerID=8YFLogxK

U2 - 10.1016/j.rinam.2025.100585

DO - 10.1016/j.rinam.2025.100585

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:105006876714

SN - 2590-0374

VL - 26

JO - Results in Applied Mathematics

JF - Results in Applied Mathematics

M1 - 100585

ER -

Functional dimensionality of Koopman eigenfunction space

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this