Physical measures of asymptotically autonomous dynamical systems

Abstract

Although chaotic attractors for autonomous dynamical systems show sensitive dependence on initial conditions, they also typically support a physical or natural measure that characterises the statistical behaviour of almost all initial conditions near the attractor with respect to a background measure such as Lebesgue. In this paper, we identify conditions under which a nonautonomous system that limits as $t \to -\infty$ to an autonomous system with a physical measure is guaranteed to possess a ``nonautonomous physical measure'' that limits to the physical measure of the autonomous system.