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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.03709 |
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Table of 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.