{"paper":{"title":"Minimality of p-adic rational maps with good reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ai-Hua Fan (LAMFA), Lingmin Liao (LAMA), Shilei Fan (CCNU), Yuefei Wang (AMSS)","submitted_at":"2015-11-16T08:01:46Z","abstract_excerpt":"A rational map with good reduction in the field $\\mathbb{Q}\\_p$ of $p$-adic numbers defines a $1$-Lipschitz dynamical system on the projective line $\\mathbb{P}^1(\\mathbb{Q}\\_p)$ over  $\\mathbb{Q}\\_p$. The dynamical structure of such a system is completely described by a minimal decomposition. That is to say, $\\mathbb{P}^1(\\mathbb{Q}\\_p)$ is decomposed into three parts:  finitely many periodic orbits; finite or countably many minimal subsystems each consisting of a finite union of balls; and the attracting basins of  periodic orbits and minimal subsystems. For any prime $p$, a criterion of mini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04856","kind":"arxiv","version":2},"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"}