Denis Sipp
ONERA – 🇫🇷 Palaiseau (France)
Koopman representations of decaying correlations: A deterministic route from continuous spectra to finite pole models
Decaying correlations in chaotic deterministic systems cannot generally be described by damped Koopman eigenfunctions in the natural space, since the Koopman group is unitary and its generator is skew-adjoint. This presentation examines how finite-dimensional models with damped poles nevertheless emerge from such dynamics. Two complementary routes are developed: meromorphic continuation of the weak correlation resolvent, leading to Ruelle–Pollicott resonances, and Mori–Zwanzig projection, where unresolved dynamics generate a memory term. Rational approximation of either the continued resolvent or the memory kernel then yields a finite realization of the correlation dynamics. The framework is illustrated using cavity-flow measurements, with particular attention to distinguishing robust isolated resonances from finite-order approximations of a continuous spectral background.