{mathbb{Z}}-Actions on AH Algebras and {mathbb{Z}^2}-Actions on AF Algebras

We consider mathbbZ{mathbb{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 mathbbZ{mathbb{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 mathbbZ²{mathbb{Z}^2}-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.