A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the union of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an autonomous map, properties that the nonautonomous attractor inherits from the autonomous attractor are discussed. Examples from population biology are presented. © 2003 Elsevier Inc. All rights reserved.
Franke, J. E., & Selgrade, J. F. (2003). Attractors for discrete periodic dynamical systems. Journal of Mathematical Analysis and Applications, 286(1), 64–79. https://doi.org/10.1016/S0022-247X(03)00417-7