Nonstationary open dynamical systems

Abstract

This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as the holes) may vary with time. Unlike the setting of random dynamical systems, no assumptions are made about the statistics of this variability. We formulate general results that yield conditional memory loss (an analog of decay of correlations) at exponential rates for nonstationary open dynamical systems. We apply our results to a class of nonstationary piecewise-smooth expanding systems in higher dimension with moving holes.