Bollt, Erik M.Ross, Shane D.2021-11-112021-11-112021-10-28Bollt, E.M.; Ross, S.D. Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction? Mathematics 2021, 9, 2731.http://hdl.handle.net/10919/106616This 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.application/pdfenCreative Commons Attribution 4.0 InternationalKoopman operatorspectral analysisinvariant manifoldsLyapunov exponentdynamical systemsArticle - Refereed2021-11-11https://doi.org/10.3390/math9212731