Fernandez and Demers studied the statistical properties of the Manneville-Pomeau
map with the physical measure when a hole is put in the system, overcoming some of
the problems caused by subexponential mixing. I’ll discuss the same setup, but with a
class of natural equilibrium states. We find conditionally invariant measures and give
precise information on the transitions between the fast exponentially mixing, the slow
exponentially mixing and the subexponentially mixing phases. This is joint work with
Mark Demers.