{"paper":{"title":"Polynomial skew products with small relative degree","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Charles Favre, Matteo Ruggiero, Romain Dujardin","submitted_at":"2025-07-12T08:29:33Z","abstract_excerpt":"We investigate the local dynamics of a proper superattracting holomorphic germ $f$ in $(\\mathbb{C}^2,0)$ possessing a totally invariant line $L$ such that $f^*L = d L$ with $d\\ge 2$, and such that $f|_L$ has a superattracting fixed point at $0$ of order $2 \\le c < d$. We prove that any such map is formally conjugated to a skew product of the form $(z^d, P(z,w))$, where $P \\in \\mathbb{C}[[z]][w]$ is polynomial in $w$ of degree $c$, hence it induces a natural dynamics on the Berkovich affine line over $\\mathbb{C}(\\!(z)\\!)$. Such non-Archimedean skew products were recently studied by Birkett and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09197","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/2507.09197/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"}