{"paper":{"title":"Rank-two recurrence results for polynomials and questions of dynamical Mordell--Lang type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO","math.NT"],"primary_cat":"math.DS","authors_text":"Geng-Rui Zhang","submitted_at":"2026-05-26T14:13:28Z","abstract_excerpt":"Let $f,g\\in\\mathbb{C}[z]\\setminus\\mathbb{C}$ and $c\\in\\mathbb{C}[z]$. Suppose that $\\mathrm{deg}(c)=1$ if $\\mathrm{deg}(f)=\\mathrm{deg}(g)=1$. Using the theory of Presburger arithmetic, we prove that the rank-two recurrence set\n  \\[S_{f,g,c}^2:=\\left\\lbrace(m,n)\\in\\mathbb{Z}_{\\geq0}^2\\colon \\exists\\lambda\\in\\mathbb{C}, f^{\\circ m}(\\lambda)=g^{\\circ n}(\\lambda)=c(\\lambda)\\right\\rbrace\\] is semi-linear. This is a generalization of a theorem of Yang and Zhong for the case $m=n$. We also obtain partial results on recurrence sets for rational maps in the case $m=n$. These results are related to hig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27058","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.27058/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"}