Transitions and anti-integrable limits for multi-hole Sturmian systems and Denjoy counterexamples. II. A gallery

In this paper, we present explicit examples of Denjoy minimal sets that exhibit two- to one-hole transitions at some parameter values 0<ϵ<1 and cantorus to circle transitions as ϵ→1 and collapse to finite sets as ϵ→0. The limit ϵ→0 is an anti-integrable limit in the sense of Aubry. We describe all the transitions in terms of multi-hole Sturmian symbolic systems.