Attractors for discrete periodic dynamical systems.
The paper introduces a notion of an attractor for a discrete time periodic dynamical system, given by~\(p\) maps \(f_0,\ldots,f_{p-1}\) on a metric space~\(X\), by extending the system to \(\{0,\ldots,p-1\}\times X\). It is shown that such an attractor is the union of attractors for the~\(p\) autonomous maps \(F_i=f_{p-1+i}\circ\cdots\circ f_i\), \(0\leq i\leq p\). Conditions are given under which the constituents of an attractor of a periodic perturbation of an autonomous map are homeomorphic to the attractor of this map. Several examples, some of them originating from population dynamics, are discussed. The results fit nicely into the theory of attractors for nonautonomous and for random systems, which has been developed during the last decade.
periodic perturbations of autonomous systems
scientific article; zbMATH DE number 2003888
scientific article