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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.23133 |
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| _version_ | 1866911084832620544 |
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| author | Arosio, Leandro Larusson, Finnur |
| author_facet | Arosio, Leandro Larusson, Finnur |
| contents | We study the dynamics of generic volume-preserving automorphisms $f$ of a Stein manifold $X$ of dimension at least 2 with the volume density property. Among such $X$ are all connected linear algebraic groups (except $\mathbb{C}$ and $\mathbb{C}^*$) with a left- or right-invariant Haar form. We show that a generic $f$ is chaotic and of infinite topological entropy, and that the transverse homoclinic points of each of its saddle periodic points are dense in $X$. We present analogous results with similar proofs in the non-conservative case. We also prove the Kupka-Smale theorem in the conservative setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic conservative dynamics on Stein manifolds with the volume density property Arosio, Leandro Larusson, Finnur Complex Variables Dynamical Systems We study the dynamics of generic volume-preserving automorphisms $f$ of a Stein manifold $X$ of dimension at least 2 with the volume density property. Among such $X$ are all connected linear algebraic groups (except $\mathbb{C}$ and $\mathbb{C}^*$) with a left- or right-invariant Haar form. We show that a generic $f$ is chaotic and of infinite topological entropy, and that the transverse homoclinic points of each of its saddle periodic points are dense in $X$. We present analogous results with similar proofs in the non-conservative case. We also prove the Kupka-Smale theorem in the conservative setting. |
| title | Generic conservative dynamics on Stein manifolds with the volume density property |
| topic | Complex Variables Dynamical Systems |
| url | https://arxiv.org/abs/2507.23133 |