MINIMAL SELF-JOININGS AND POSITIVE TOPOLOGICAL-ENTROPY

We show that the properties of almost minimal self-joinings and strong almost minimal self-joinings, introduced by del Junco in Topological Dynamics, are compatible with positive topological entropy, as opposed to the stronger property of minimal self-joinings. This is done both by proving existence theorems and by explicitly constructing some symb olic systems having these properties, which are modifications of the C hacon system. It is shown furthermore that these systems have no non-t rivial factors with completely positive topological entropy.