Generic aspects of holomorphic dynamics on highly flexible complex manifolds
11 Oct 2019
•
Arosio Leandro
•
Larusson Finnur
We 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 Fornaess and Sibony: our main results generalise
theorems of theirs and we use their methods of proof.(read more)