Is the FiniteTime Lyapunov Exponent Field a Koopman Eigenfunction?
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.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12163
 Bibcode:
 2021arXiv210912163B
 Keywords:

 Mathematics  Dynamical Systems;
 Condensed Matter  Statistical Mechanics;
 Mathematics  Spectral Theory;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 30 pages, 4 figures