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

Erik M. Bollt and Shane D. Ross
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Erik M. Bollt: Electrical & Computer Engineering & C 3 S 2 , The Clarkson Center for Complex Systems Science, Clarkson University, Potsdam, NY 13699, USA
Shane D. Ross: Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, VA 24061, USA

Mathematics, 2021, vol. 9, issue 21, 1-20

Abstract: 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.

Keywords: Koopman operator; spectral analysis; invariant manifolds; Lyapunov exponent; dynamical systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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