Dynamics of generic automorphisms of Stein manifolds with the density property
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916740504485888 |
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| author | Arosio, Leandro Larusson, Finnur |
| author_facet | Arosio, Leandro Larusson, Finnur |
| contents | 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 $\mathbb C^n$, $n\geq 2$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05002 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamics of generic automorphisms of Stein manifolds with the density property Arosio, Leandro Larusson, Finnur Complex Variables Dynamical Systems Primary 32H50. Secondary 14R10, 32M17, 32Q28, 37F80 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 $\mathbb C^n$, $n\geq 2$, 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. |
| title | Dynamics of generic automorphisms of Stein manifolds with the density property |
| topic | Complex Variables Dynamical Systems Primary 32H50. Secondary 14R10, 32M17, 32Q28, 37F80 |
| url | https://arxiv.org/abs/2303.05002 |