Generic aspects of holomorphic dynamics on highly flexible complex manifolds
| Autor: | Finnur Larusson, Leandro Arosio |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Chaotic automorphism
Pure mathematics Property (philosophy) Endomorphism Holomorphic function Periodic point Stein manifold Oka manifold Density property Volume density property Linear algebraic group Dynamics Non-wandering point Closing lemma Dynamical Systems (math.DS) 01 natural sciences 0103 physical sciences FOS: Mathematics Mathematics - Dynamical Systems 0101 mathematics Complex Variables (math.CV) Mathematics::Symplectic Geometry Mathematics Mathematics - Complex Variables Mathematics::Complex Variables Applied Mathematics 010102 general mathematics 32M17 (Primary) 14L17 14R10 14R20 32H50 32M05 32Q28 37F99 (Secondary) Automorphism Mathematics::Geometric Topology Manifold Settore MAT/03 010307 mathematical physics |
| DOI: | 10.48550/arxiv.1910.01418 |
| Popis: | 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. Comment: Version 2: Several minor improvements |
| Databáze: | OpenAIRE |
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