Ábel Komálovics: ACIM instability of one-dimensional expanding maps through the lens of metastability
If we have a family of expanding maps with unique ACIMs, then the ACIM stability of the family means that if the maps are converging to a limit map, then the densities converge to the density of the limit map. There are multiple papers showcasing ACIM instability, but all of them use methods specific to the families introduced in the papers. We develop a unified framework that allows us to use the tools of analysis of metastable maps. This way we can calculate the limit density, the finite dimensional distribution of the wandering of points and the diffusion coefficient.