Pseudo-orbits, stationary measures and metastability

W Bahsoun (1) , H Hu (2) , S Vaienti (3, 4)

1 Department of Mathematical Sciences, Loughborough University
2 Department of Mathematics [Lansing]
3 CPT - Ex E7 Systèmes dynamiques et théorie ergodique
4 CPT - Centre de Physique Théorique - UMR 7332

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 continuous 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 is in a one-to-one correspondence with an ergodic acsm of the random system. Moreover our result permits to identify random perturbations that exhibit a metastable behavior.

Domaines: Systèmes dynamiques [math.DS]

W Bahsoun, H Hu, S Vaienti. Pseudo-orbits, stationary measures and metastability. Dynamical Systems, 2014, 29 (3), pp.322-336. ⟨10.1080/14689367.2014.890172⟩. ⟨hal-01126704⟩