{"paper":{"title":"Polynomial compositions with large monodromy groups and applications to arithmetic dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Danny Neftin, Joachim K\\\"onig, Shai Rosenberg","submitted_at":"2024-01-31T14:28:58Z","abstract_excerpt":"For a composition $f=f_1\\circ\\cdots \\circ f_r$ of polynomials $f_i\\in \\mathbb Q[x]$ of degrees $d_i\\geq 5$ with alternating or symmetric monodromy group, we show that the monodromy group of $f$ contains the iterated wreath product $A_{d_r}\\wr \\cdots\\wr A_{d_1}$. A similar property holds more generally for polynomials that do not factor through $x^d$ or Chebyshev. We derive consequences to arithmetic dynamics regarding arboreal representations, and forward and backward orbits of such $f$. In particular, given an orbit $(a_n)_{n=0}^\\infty$ of $f$ as above, we show that for \"almost all\" $a\\in \\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.17872","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.17872/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}