Skew-product dynamical systems: Applications to difference equations

Skew-Product Dynamical Dystems: Applications to Difference Equations

Integral Equations and Exponential Trichotomy of Skew-Product Flows

We are interested in an open problem concerning the integral characterizations of the uniform exponential trichotomy of skew-product flows. We introduce a new admissibility concept which relies on a double solvability of an associated integral equation and prove that this provides several interesting asymptotic properties. The main results will establish the connections between this new admissi...

Minimal attractors and bifurcations of random dynamical systems

We consider attractors for certain types of random dynamical systems. These are skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors and invariant measures for deterministic and random dynamical systems. Under assumptions that include, for example, iterated function systems, but that exclude stochastic differ...

On the computation of invariant measures in random dynamical systems

Invariant measures of dynamical systems generated e. g. by difference equations can be computed by discretizing the originally continuum state space, and replacing the action of the generator by the transition mechanism of a Markov chain. In fact they are approximated by stationary vectors of these Markov chains. Here we extend this well known approximation result and the underlying algorithm t...

Fractional dynamical systems: A fresh view on the local qualitative theorems

The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...