{"paper":{"title":"Dynamically distinguishing polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Andrew Bridy, Derek Garton","submitted_at":"2016-09-29T03:14:01Z","abstract_excerpt":"A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: for any prime $p$, reduce its coefficients mod $p$ and consider its action on the field $\\mathbb{F}_p$. We say a subset of $\\mathbb{Z}[x]$ is dynamically distinguishable mod $p$ if the associated mod $p$ dynamical systems are pairwise non-isomorphic. For any $k,M\\in\\mathbb{Z}_{>1}$, we prove that there are infinitely many sets of integers $\\mathcal{M}$ of size $M$ such that $\\left\\{ x^k+m\\mid m\\in\\mathcal{M}\\right\\}$ is dynamically distinguishable mod $p$ for most $p$ (in the sense of natu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09186","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"}