Mathematics (Oct 2021)

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

  • Erik M. Bollt,
  • Shane D. Ross

DOI
https://doi.org/10.3390/math9212731
Journal volume & issue
Vol. 9, no. 21
p. 2731

Abstract

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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