Metastability of Certain Intermittent Maps

Wael Bahsoun , Sandro Vaienti (1, 2)

1 CPT - Ex E7 Systèmes dynamiques et théorie ergodique
2 CPT - Centre de Physique Théorique - UMR 7332

We study an intermittent map which has exactly two ergodic invariant densities. The densities are supported on two subintervals with a common boundary point. Due to certain perturbations, leakage of mass through subsets, called holes, of the initially invariant subintervals occurs and forces the subsystems to merge into one system that has exactly one invariant density. We prove that the invariant density of the perturbed system converges in the $L^1$-norm to a particular convex combination of the invariant densities of the intermittent map. In particular, we show that the ratio of the weights in the combination equals to the limit of the ratio of the measures of the holes.

Domaines: Systèmes dynamiques [math.DS]

Wael Bahsoun, Sandro Vaienti. Metastability of Certain Intermittent Maps. Nonlinearity, 2012, 25, pp.107-124. ⟨10.1088/0951-7715/25/1/107⟩. ⟨hal-00975711⟩