Z-actions on AH algebras and Z2-actions on AF algebras

We consider Z-actions (single automorphisms) on a unital simple AH algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the Rohlin property under some technical assumptions. Moreover, two Z-actions with the Rohlin property on such a C∗-algebra are shown to be cocycle conjugate if they are asymptotically unitarily equivalent. We also prove that locally approximately inner and uniformly outer Z2-actions on a unital simple AF algebra with a unique trace have the Rohlin property and classify them up to cocycle conjugacy employing the OrderExt group as classification invariants.