Koopman eigenvalues and PSD for a noise-free Duffing oscillator (D = 0, δ = 0.2, α = −1.2, β = 0.9, γ = 1.0, Ω = 0.6). Top: light curve showing quasiperiodic behavior. Bottom left: eigenvalues of ﹩{ \mathcal L }﹩ in the complex plane; 2 × 13 eigenvalues lie near the imaginary axis (highlighted: red and green). Bottom right: PSD with 13 narrow QPOs; vertical lines mark frequencies corresponding to the highlighted eigenvalues.