Perron—frobenius Spectrum for Random Maps and Its Approximation

Spectrum Properties of the Koopman and Frobenius-Perron Operators

Characterization of Chaos in Random Maps

We discuss the characterization of chaotic behaviours in random maps both in terms of the Lyapunov exponent and of the spectral properties of the Perron-Frobenius operator. In particular, we study a logistic map where the control parameter is extracted at random at each time step by considering nite dimensional approximation of the Perron-Frobenius operator.

Metastability, Lyapunov Exponents, Escape Rates, and Topological Entropy in Random Dynamical Systems

We explore the concept of metastability in random dynamical systems, focusing on connections between random Perron–Frobenius operator cocycles and escape rates of random maps, and on topological entropy of random shifts of finite type. The Lyapunov spectrum of the random Perron–Frobenius cocycle and the random adjacency matrix cocycle is used to decompose the random system into two disjoint ran...

On Ulam Approximation of the Isolated Spectrum and Eigenfunctions of Hyperbolic Maps

Perron-Frobenius operators and their eigendecompositions are increasingly being used as tools of global analysis for higher dimensional systems. The numerical computation of large, isolated eigenvalues and their corresponding eigenfunctions can reveal important persistent structures such as almostinvariant sets, however, often little can be said rigorously about such calculations. We attempt to...

Ruelle-perron-frobenius Spectrum for Anosov Maps

We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the transfer operator is quasicompact. (In...