On the algebra of Koopman eigenfunctions and on some of their infinities

ArXi:2604.21825v1 Announce Type: cross 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.