Approximation of attractors of nonautonomous dynamical systems (Q558579)

Let \(\phi\) be a flow on a metric space \(X\). The authors introduce and study the following important notion. An invariant set \(A\subset X\) is said to be compactly generated if there exists a compact set \(K\subset X\) with the following property: for any compact set \(C\subset X\) there exists a \(T(K,C)>0\) such that \(A\cap C\subset \phi(t,A\cap K)\) for \(t>T(K,C)\). This notion is generalized to the case of nonautonomous dynamical systems. The authors describe several numerical algorithms for the approximation of compactly generated attractors for such systems. The algorithms are applied to a two-dimensional system of nonautonomous difference equations. An example of application of the methods to the Duffing-Van der Pol oscillator is presented.