Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?

This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field is a Koopman eigenfunction. Restricting ourse...

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Autores principales:	Erik M. Bollt, Shane D. Ross
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Koopman operator spectral analysis invariant manifolds Lyapunov exponent dynamical systems Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/30f66abf12b648debe51bb17f53fbb57
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spelling	oai:doaj.org-article:30f66abf12b648debe51bb17f53fbb572021-11-11T18:16:57ZIs the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?10.3390/math92127312227-7390https://doaj.org/article/30f66abf12b648debe51bb17f53fbb572021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2731https://doaj.org/toc/2227-7390This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field is a Koopman eigenfunction. Restricting ourselves to polynomial vector fields to make this construction easier, we find that such vector fields do exist, and we explore whether such vector fields have a special structure, thus making a link between the geometric theory and the transfer operator theory.Erik M. BolltShane D. RossMDPI AGarticleKoopman operatorspectral analysisinvariant manifoldsLyapunov exponentdynamical systemsMathematicsQA1-939ENMathematics, Vol 9, Iss 2731, p 2731 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Koopman operator spectral analysis invariant manifolds Lyapunov exponent dynamical systems Mathematics QA1-939
spellingShingle	Koopman operator spectral analysis invariant manifolds Lyapunov exponent dynamical systems Mathematics QA1-939 Erik M. Bollt Shane D. Ross Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?
description	This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field is a Koopman eigenfunction. Restricting ourselves to polynomial vector fields to make this construction easier, we find that such vector fields do exist, and we explore whether such vector fields have a special structure, thus making a link between the geometric theory and the transfer operator theory.
format	article
author	Erik M. Bollt Shane D. Ross
author_facet	Erik M. Bollt Shane D. Ross
author_sort	Erik M. Bollt
title	Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?
title_short	Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?
title_full	Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?
title_fullStr	Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?
title_full_unstemmed	Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?
title_sort	is the finite-time lyapunov exponent field a koopman eigenfunction?
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/30f66abf12b648debe51bb17f53fbb57
work_keys_str_mv	AT erikmbollt isthefinitetimelyapunovexponentfieldakoopmaneigenfunction AT shanedross isthefinitetimelyapunovexponentfieldakoopmaneigenfunction
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Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?

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