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 Pseudo-Orbits, Stationary Measures and Metastability


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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.



Author: Wael Bahsoun; Huyi Hu; Sandro Vaienti

Source: https://archive.org/



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