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arXiv · 1211.2952

Pseudo-Orbits, Stationary Measures and Metastability

Wael Bahsoun·Huyi Hu·Sandro Vaienti
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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.

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Wael Bahsoun, Huyi Hu, Sandro Vaienti. 2014-01-29. Pseudo-Orbits, Stationary Measures and Metastability. https://arxiv.org/abs/1211.2952

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