# Anti-Koopmanism

@article{Gonzlez2021AntiKoopmanism, title={Anti-Koopmanism}, author={Efra{\'i}n Gonz{\'a}lez and Moad Abudia and Michael T. Jury and Rushikesh Kamalapurkar and Joel A. Rosenfeld}, journal={ArXiv}, year={2021}, volume={abs/2106.00106} }

This article addresses several longstanding misconceptions concerning Koopman operators, including the existence of lattices of eigenfunctions, common eigenfunctions between Koopman operators, and boundedness and compactness of Koopman operators, among others. Counterexamples are provided for each misconception. This manuscript also proves that the Gaussian RBF’s native space only supports bounded Koopman operator corresponding to affine dynamics, which shows that the assumption of boundedness…

## 3 Citations

Singular Dynamic Mode Decompositions

- Computer Science, EngineeringArXiv
- 2021

This manuscript concludes with the description of a Dynamic Mode Decomposition algorithm that converges when a dense collection of occupation kernels, arising from the data, are leveraged in the analysis.

Koopman Operator Theory for Nonlinear Dynamic Modeling using Dynamic Mode Decomposition

- Computer Science, MathematicsArXiv
- 2021

A brief summary of the Koopman operator theorem for nonlinear dynamics modeling is provided and several data-driven implementations using dynamical mode decomposition (DMD) for autonomous and controlled canonical problems are analyzed.

Deep Learning Enhanced Dynamic Mode Decomposition

- Computer Science, MathematicsArXiv
- 2021

This work explores the use of convolutional autoencoder networks to simultaneously find optimal families of observables and results in a global transformation of the flow that affords future state prediction via EDMD and the decoder network and is shown to produce results that outperform a standard DMD approach.

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