Measure theory and Perron-Frobenius operators for continued fractions

Weighted Frobenius-Perron and Koopman operators

Spectrum Properties of the Koopman and Frobenius-Perron Operators

Compact weighted Frobenius-Perron operators and their spectra

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.

Perron—frobenius Spectrum for Random Maps and Its Approximation

To study the convergence to equilibrium in random maps, we develop the spectral theory of the corresponding transfer (Perron— Frobenius) operators acting in a certain Banach space of generalized functions (distributions). The random maps under study in a sense fill the gap between expanding and hyperbolic systems, since among their (deterministic) components there are both expanding and contrac...