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

@article{Bollt2021IsTF,
  title={Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?},
  author={Erik M. Bollt and Shane D. Ross},
  journal={Mathematics},
  year={2021}
}
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… 
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