This paper is devoted to the study of time-varying impulsive recursive motions. We investigate the connections among minimal sets, non-wandering points, the Birkhoff center, and attractors. As an illustration, the obtained results are applied to a semilinear reaction-diffusion equation with impulses and to an integrate (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.