Arosio, L.Lárusson, F.2020-01-162020-01-162020Annali di Matematica Pura ed Applicata, 2020; 199(4):1697-17110373-31141618-1891http://hdl.handle.net/2440/122733We prove closing lemmas for automorphisms of a Stein manifold with the density property and for endomorphisms of an Oka–Stein manifold. In the former case, we need to impose a new tameness condition. It follows that hyperbolic periodic points are dense in the tame non-wandering set of a generic automorphism of a Stein manifold with the density property and in the non-wandering set of a generic endomorphism of an Oka–Stein manifold. These are the first results about holomorphic dynamics on Oka manifolds. We strengthen previous results of ours on the existence and genericity of chaotic volume-preserving automorphisms of Stein manifolds with the volume density property. We build on work of Fornæss and Sibony: our main results generalise theorems of theirs, and we use their methods of proof.en© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019Stein manifold; Oka manifold; density property; volume density property; linear algebraic group; dynamics; non-wandering point; periodic point; closing lemma; chaotic automorphismJournal article100001150510.1007/s10231-019-00938-60005011876000012-s2.0-85076228160500306