Intersection of orbits of loxodromic automorphisms of affine surfaces
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910601671868416 |
|---|---|
| author | Abboud, Marc |
| author_facet | Abboud, Marc |
| contents | We show the following result: If $X_0$ is an affine surface over a field $K$ and $f, g$ are two loxodromic automorphisms with an orbit meeting infinitely many times, then $f$ and $g$ must share a common iterate. The proof uses the preliminary work of the author in [Abb23] on the dynamics of endomorphisms of affine surfaces and arguments from arithmetic dynamics. We then show a dynamical Mordell-Lang type result for surfaces in $X_0 \times X_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intersection of orbits of loxodromic automorphisms of affine surfaces Abboud, Marc Algebraic Geometry Complex Variables Dynamical Systems Number Theory 37F10, 37F80, 37P05, 37P30, 32H50, 37P55, 11G50 We show the following result: If $X_0$ is an affine surface over a field $K$ and $f, g$ are two loxodromic automorphisms with an orbit meeting infinitely many times, then $f$ and $g$ must share a common iterate. The proof uses the preliminary work of the author in [Abb23] on the dynamics of endomorphisms of affine surfaces and arguments from arithmetic dynamics. We then show a dynamical Mordell-Lang type result for surfaces in $X_0 \times X_0$. |
| title | Intersection of orbits of loxodromic automorphisms of affine surfaces |
| topic | Algebraic Geometry Complex Variables Dynamical Systems Number Theory 37F10, 37F80, 37P05, 37P30, 32H50, 37P55, 11G50 |
| url | https://arxiv.org/abs/2409.07826 |