Tropical Dynamics of Markov Surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914207765626880 |
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| author | Jang, Seung uk |
| author_facet | Jang, Seung uk |
| contents | We discuss the algebraic dynamics on Markov cubics generated by Vieta involutions, in the tropicalized setting. It turns out that there is an invariant subset of the tropicalized Markov cubic where the action by Vieta involutions can be modeled by that of $(\infty,\infty,\infty)$-triangle reflection group on the hyperbolic plane.
This understanding of the tropicalized algebraic dynamics produces some results on Markov cubics over non-archimedean fields, including the existence of the Fatou domain and finitude of orbits with rational points having prime power denominators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11357 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tropical Dynamics of Markov Surfaces Jang, Seung uk Dynamical Systems Geometric Topology Number Theory We discuss the algebraic dynamics on Markov cubics generated by Vieta involutions, in the tropicalized setting. It turns out that there is an invariant subset of the tropicalized Markov cubic where the action by Vieta involutions can be modeled by that of $(\infty,\infty,\infty)$-triangle reflection group on the hyperbolic plane. This understanding of the tropicalized algebraic dynamics produces some results on Markov cubics over non-archimedean fields, including the existence of the Fatou domain and finitude of orbits with rational points having prime power denominators. |
| title | Tropical Dynamics of Markov Surfaces |
| topic | Dynamical Systems Geometric Topology Number Theory |
| url | https://arxiv.org/abs/2306.11357 |