Resultant measures and minimal resultant loci for non-archimedean polynomial dynamics
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866910542153646080 |
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| author | Nie, Hongming Okuyama, Yûsuke |
| author_facet | Nie, Hongming Okuyama, Yûsuke |
| contents | We compute the resultant measures for iterations $P^j$, $j\ge 1$, of a polynomial $P$ of degree $>1$ on the $n$-th level Trucco's trees $Γ_n$, $n\ge 0$, in the Berkovich projective line over a non-archimedean field and also determine their barycenters. As applications, we study the asymptotic of those barycenters as $n\to\infty$, and establish a uniform stationarity of Rumely's minimal resultant loci of $P^j$ or equivalently that of the potential semistable reduction loci of $P^j$ as $j\to\infty$. We also establish several equidistribution results for the resultant measures themselves as $n\to\infty$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2005_05804 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Resultant measures and minimal resultant loci for non-archimedean polynomial dynamics Nie, Hongming Okuyama, Yûsuke Number Theory Dynamical Systems We compute the resultant measures for iterations $P^j$, $j\ge 1$, of a polynomial $P$ of degree $>1$ on the $n$-th level Trucco's trees $Γ_n$, $n\ge 0$, in the Berkovich projective line over a non-archimedean field and also determine their barycenters. As applications, we study the asymptotic of those barycenters as $n\to\infty$, and establish a uniform stationarity of Rumely's minimal resultant loci of $P^j$ or equivalently that of the potential semistable reduction loci of $P^j$ as $j\to\infty$. We also establish several equidistribution results for the resultant measures themselves as $n\to\infty$. |
| title | Resultant measures and minimal resultant loci for non-archimedean polynomial dynamics |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2005.05804 |