Nonstandard analysis of global attractors

摘要

Key concepts of the theory of abstract dynamical systems are formulated in the language of nonstandard analysis (NSA). We are then able to provide simple and intuitive proofs of the basic facts. In particular, we use the NSA to give an alternative proof of the characterization of global attractors due to Ball. We also address the issue of connectedness. The key observation is that the global attractor, or more generally, the omega-limit set, can be written as a standard part of a suitable internal set. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim