Disjoint hypercyclic linear fractional composition operators

We characterize disjoint hypercyclicity and disjoint supercyclicity of finitely many linear fractional composition operators acting on spaces of holomorphic functions on the unit disc, answering a question of Bernal-Gonzلlez. We also study mixing and disjoint mixing behavior of projective limits of endomorphisms of a projective spectrum. In particular, we show that a linear fractional composition operator is mixing on the projective limit of the S v spaces strictly containing the Dirichlet space if and only if the operator is mixing on the Hardy space.