Finite-type boundary conjecture for stable regions

Let a stable region be a connected region in the parameter space of interval translation maps on which the maps are stable, and let its boundary consist of the maps obtained at the boundary of that region. A map is of finite type if its associated dynamical system has finite type. Finite-type boundary conjecture. Every map in the boundary of a stable region is of finite type. This rules out a bifurcation from a stable region directly to an infinite-type map and concerns the dynamical behavior on the bifurcation locus.