Chacon’s automorphism has minimal self joinings

Toeplitz subshift whose automorphism group is not finitely generated

“…6 The group A(5, 2) is the simplest interesting example obtained like this. The construction also applies to A(3, 1), but this group is isomorphic to Z.…”

“…More generally, for any triple (p, p ′ , q) satisfying (1) and p prime, we will find a Toeplitz subshift whose automorphism group (in fact, the whole endomorphism monoid) is isomorphic to the group A(p, q). 6 We make some standing assumptions for the rest of this section. We fix a triple (p, p ′ , q) satisfying (1) with p prime.…”

“…For example, the result of [18] shows that all Sturmian subshifts have an automorphism group consisting of shift maps only. For many examples, a stronger property called minimal self-joinings [12,6,21] is known, and it is easy to see that subshifts with this property cannot have automorphisms other than shift maps.…”

Weak disjointness of measure-preserving dynamical systems

“…But we know that Chacon's dynamical system has minimal self-joinings of all orders ( [5]), and we conclude that λ = λ ′ . This proves that the system is self-weakly disjoint of all orders.…”

Classifying dynamical systems by their recurrence properties

“…Finally there are mildly but not strongly mixing systems; e.g. Chacón's system is an example (see del Junco, Rahe and Swanson [23] and Aaronson and Weiss [1]). …”