2023/03/09 by Leandro Arosio, Finnur Lárusson, Arosio, Leandro +1 · 2 citations
Mathematics · #32M17 #32Q28 #37F80 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Primary 32H50. Secondary 14R10
paper · pdf · doi:10.48550/arxiv.2303.05002
openalex publication_date 2023/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the dynamics of a generic automorphism f of a Stein manifold with the density property. Such manifolds include all linear algebraic groups. Even in the special case of \mathbb Cn, n≥ 2, most of our results are new. We study the Julia set, non-wandering set, and chain-recurrent set of f. We show that the closure of the set of saddle periodic points of f is the largest forward invariant set on which f is chaotic. This subset of the Julia set of f is also characterised as the closure of the set of transverse homoclinic points of f, and equals the Julia set if and only if a certain closing lemma holds. Among the other results in the paper is a generalisation of Buzzard's holomorphic Kupka-Smale theorem to our setting.