Semistable intrinsic reduction loci for the iterations of non-archimedean quadratic rational functions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911517348200448 |
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| author | Okuyama, Yûsuke |
| author_facet | Okuyama, Yûsuke |
| contents | We introduce a semistability notion of the intrinsic reductions of a non-archimedean rational function at each non-classical point in the Berkovich projective line, which extends the potential GIT-semistability one defined at each type II points, and compute the intrinsic semistability loci for the iterations of a quadratic rational function using a reduction theoretic slope formula for the hyperbolic resultant function associated to those iterations. In particular, we establish a precise stationarity of those loci for iterated quadratic rational functions similar to that in the case of non-archimedean polynomial dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03709 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semistable intrinsic reduction loci for the iterations of non-archimedean quadratic rational functions Okuyama, Yûsuke Number Theory Dynamical Systems We introduce a semistability notion of the intrinsic reductions of a non-archimedean rational function at each non-classical point in the Berkovich projective line, which extends the potential GIT-semistability one defined at each type II points, and compute the intrinsic semistability loci for the iterations of a quadratic rational function using a reduction theoretic slope formula for the hyperbolic resultant function associated to those iterations. In particular, we establish a precise stationarity of those loci for iterated quadratic rational functions similar to that in the case of non-archimedean polynomial dynamics. |
| title | Semistable intrinsic reduction loci for the iterations of non-archimedean quadratic rational functions |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2603.03709 |