Pseudo-orbits, stationary measures and metastability

• Published in: Dynamical systems (London, England) Vol. 29; no. 3; pp. 322 - 336
• Main Authors: Bahsoun, Wael, Hu, Huyi, Vaienti, Sandro
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 03-07-2014
• Subjects: Banach space; Dynamical Systems; Dynamics; Ergodic processes; expanding maps; Inequalities; Invariants; Joining; Mathematics; Metastability; Primary 37A05; pseudo-orbits; random perturbations
• ISSN: 1468-9367; 1468-9375
• DOI: 10.1080/14689367.2014.890172

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.