Metastability and Dominant Eigenvalues of Transfer Operators

Near Invariance and Local Transience for Random Diffeomorphisms

Nearly (or almost) invariant sets for random dynamical systems are subsets of the state space that are left only after long time and, maybe, are visited again after even longer times. The present paper takes up the approach developed in Colonius, Gayer, and Kliemann [8] for Markov diffusions. We develop an analogous theory for random diffeomorphisms and also use results from Zmarrou and Homburg...

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Towards Effective Dynamics in Complex Systems by Markov Kernel Approximation

Many complex systems occurring in various application share the property that the underlying Markov process remains in certain regions of the state space for long times, and that transitions between such metastable sets occur only rarely. Often the dynamics within each metastable set is of minor importance, but the transitions between these sets are crucial for the behavior and the understandin...

Stability of the spectrum for transfer operators

We prove stability of the isolated eigenvalues of transfer operators satisfying a Lasota-Yorke type inequality under a broad class of random and nonrandom perturbations including Ulam-type discretizations. The results are formulated in an abstract framework.