{"paper":{"title":"$p$-adic dynamical systems of $(2,2)$-rational functions with unique fixed point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"I.A. Sattarov, U.A. Rozikov","submitted_at":"2017-03-27T10:51:04Z","abstract_excerpt":"We consider a family of $(2,2)$-rational functions given on the set of complex $p$-adic field $\\mathbb{C}_p$. Each such function has a unique fixed point. We study $p$-adic dynamical systems generated by the $(2,2)$-rational functions. We show that the fixed point is indifferent and therefore the convergence of the trajectories is not the typical case for the dynamical systems. Siegel disks of these dynamical systems are found.\n  We obtain an upper bound for the set of limit points of each trajectory, i.e., we determine a sufficiently small set containing the set of limit points. For each $(2,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09001","kind":"arxiv","version":1},"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"}