On the algebra of Koopman eigenfunctions and on some of their infinities
For continuous-time dynamical systems with reversible trajectories, the nowhere-vanishing eigenfunctions of the Koopman operator of the system form a multiplicative group. Here, we exploit this property to accelerate the systematic numerical computation of the eigenspaces of the operator. Given a small set of (so-called ``principal'') eigenfunctions that are approximated conventionally, we can obtain a much larger set by constructing polynomials of the principal eigenfunctions. This enriches the set, and thus allows us to more accurately represent application-specific observables. Often, eigenfunctions exhibit localized singularities (e.g. in simple, one-dimensional problems with multiple...
| Authors | Zahra Monfared, Saksham Malhotra, Sekiya Hajime et al. |
|---|---|
| Primary category | math.DS |
| Published | 23 April 2026 |
| Last updated at source | 23 April 2026 |
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