{"paper":{"title":"Exponential-polynomial equations and dynamical return sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.DS","authors_text":"Thomas Scanlon, Yu Yasufuku","submitted_at":"2012-12-08T21:30:07Z","abstract_excerpt":"We show that for each finite sequence of algebraic integers $\\alpha_1,...,\\alpha_n$ and polynomials $P_1(x_1,...,x_n;y_1,...,y_n),..., P_r(x_1,...,x_n;y_1,...,y_n)$ with algebraic integer coefficients, there are a natural number $N$, $n$ commuting endomorphisms $\\Phi_i:\\Gm^N \\to \\Gm^N$ of the $N^\\text{th}$ Cartesian power of the multiplicative group, a point $P \\in \\Gm^N(\\QQ)$, and an algebraic subgroup $G \\leq \\Gm^N$ so that the return set $\\{(\\ell_1,...,\\ell_n) \\in \\NN^n : \\Phi_1^{\\circ \\ell_1} \\circ... \\circ \\Phi_n^{\\circ \\ell_n}(P) \\in G(\\QQ) \\}$ is identical to the set of solutions to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1836","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"}