On the numerical approximation of the Perron-Frobenius and Koopman operator

Spectrum Properties of the Koopman and Frobenius-Perron Operators

Weighted Frobenius-Perron and Koopman operators

Stochastic Properties of the Frobenius-perron Operator

In the present paper the Renormalization Group (RG) method is adopted as a tool for a constructive analysis of the properties of the Frobenius-Perron Operator. The renormalization group reduction of a generic symplectic map in the case, where the unperturbed rotation frequency of the map is far from structural resonances driven by the kick perturbation has been performed in detail. It is furthe...

weighted frobenius-perron and koopman operators

On the isolated spectrum of the Perron–Frobenius operator

We discuss the existence of large isolated (non-unit) eigenvalues of the Perron– Frobenius operator for expanding interval maps. Corresponding to these eigenvalues (or ‘resonances’) are distributions which approach the invariant density (or equilibrium distribution) at a rate slower than that prescribed by the minimal expansion rate. We consider the transitional behaviour of the eigenfunctions ...