A Note on Double Minimality

Abstract

It is known that a minimal prime system is either a subshift or with a connected phase space (Keynes and Newton Trans Am Math Soc 217:237–255, 1976). We show that a double minimal system is a subshift; this implies immediately that no non-periodic map has 4-fold topological minimal self-joinings. We also prove that a POD system is either uniformly rigid or is a subshift.