{"paper":{"title":"Degenerations of Complex Dynamical Systems II: Analytic and Algebraic Stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Laura DeMarco, with an appendix by Jan Kiwi, Xander Faber","submitted_at":"2013-09-27T02:50:06Z","abstract_excerpt":"We study pairs $(f, \\Gamma)$ consisting of a non-Archimedean rational function $f$ and a finite set of vertices $\\Gamma$ in the Berkovich projective line, under a certain stability hypothesis. We prove that stability can always be attained by enlarging the vertex set $\\Gamma$. As a byproduct, we deduce that meromorphic maps preserving the fibers of a rationally-fibered complex surface are algebraically stable after a proper modification. The first article in this series examined the limit of the equilibrium measures for a degenerating 1-parameter family of rational functions on the Riemann sph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7103","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}