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 characterizes the statistical behavior 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 [Formula: see text] 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.