%0 Journal Article %A Bahsoun, Wael %A Hu, Huyi %A Vaienti, Sandro %D 2016 %T Pseudo-orbits, stationary measures and metastability %U https://repository.lboro.ac.uk/articles/journal_contribution/Pseudo-orbits_stationary_measures_and_metastability/9385130 %2 https://repository.lboro.ac.uk/ndownloader/files/16998323 %K untagged %K Mathematical Sciences not elsewhere classified %X We characterize absolutely continuous stationary measures (acsms) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of absolutely continuous invariant measures (acims) of the unperturbed system. We focus on those components, called least elements, which attract pseudo-orbits. Under the assumption that the transfer operators of both systems, the random and the unperturbed, satisfy a uniform Lasota-Yorke inequality on a suitable Banach space, we show that each least element is in a one-to-one correspondence with an ergodic acsm of the random system. %I Loughborough University