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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Erik M. Bollt & Shane D. Ross, 2021. "Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?," Mathematics, MDPI, vol. 9(21), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2731-:d:666458
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