Measure and Statistical Attractors for Nonautonomous Dynamical Systems

Abstract Various inequivalent notions of attraction for autonomous dynamical systems have been proposed, each them useful to understand specific aspects attraction. Milnor’s notion a measure attractor considers invariant sets with positive basin attraction, while Ilyashenko’s weaker statistical points that approach the set in terms averages. In this paper we propose generalisations these nonautonomous evolution processes continuous time. We demonstrate pullback/forward measure/statistical attractors can be defined an analogous manner and relate respective when system is considered as nonautonomous. There are some subtleties even special case–we illustrate example two-dimensional flow one-dimensional containing single point attractor. show pullback system. Finally, particular case asymptotically (where there future past limit systems) (respectively, forward) future) systems.