BAHSOUN, W. and VAIENTI, S., 2012. Metastability of Certain Intermittent Maps. Nonlinearity, 25 (1), pp.107-124.
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 L1-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 is
equal to the limit of the ratio of the measures of the holes.
S.V. was supported by the ANR-grant Perturbations.