Pseudo-Orbits, Stationary Measures and Metastability

Abstract

We study random perturbations of multidimensional piecewise expanding maps. We characterize absolutely continuous stationary measures (acsm) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of absolutely invariant measures (acim) of the unperturbed system. We focus on those components, called least-elements, which attract pseudo-orbits. We show that each least element admits a neighbourhood which supports exactly one ergodic acsm of the random system. We use this result to identify random perturbations that exhibit a metastable behavior.

To appear in Dynamical Systems

References in corpus (3)

• Laws of rare events for deterministic and random dynamical systems
• Escape Rates Formulae and Metastability for Randomly perturbed maps
• Representation of Markov chains by random maps: existence and regularity conditions